Number of the day: 79103

Properties of the number 79103:

79103 is a cyclic number.
79103 is the 7752^th prime.
79103 has 21 antidivisors and 79102 totatives.
79103 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 79103 results in an emirp.
79103 = 39552² - 39551² is the difference of 2 nonnegative squares in 1 way.
79103 is the difference of 2 positive pentagonal numbers in 1 way.
79103 is not the sum of 3 positive squares.
79103² is the sum of 3 positive squares.
79103 is a proper divisor of 2³⁹⁵⁵¹ - 1.
79103 = '7' + '9103' is the concatenation of 2 prime numbers.
79103 is an emirp in (at least) the following bases: 2, 6, 7, 10, 15, 17, 23, 24, 27, 29, 41, 49, 52, 55, 58, 59, 65, 67, 69, 73, 76, 77, and 100.

The number 79103 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A113893: Smallest prime obtained as a concatenation of prime(n) and prime(m) with m > n.

Number of the day: 56493

Properties of the number 56493:

56493 = 3² × 6277 is the 50764^th composite number and is not squarefree.
56493 has 2 distinct prime factors, 6 divisors, 13 antidivisors and 37656 totatives.
56493 has a triangular digit product 3240 in base 10.
56493 = 2³ + 18³ + 37³ is the sum of 3 positive cubes in 1 way.
56493 = 28247² - 28246² = 9417² - 9414² = 3143² - 3134² is the difference of 2 nonnegative squares in 3 ways.
56493 is the difference of 2 positive pentagonal numbers in 1 way.
56493 = 18² + 237² is the sum of 2 positive squares in 1 way.
56493 = 11² + 26² + 236² is the sum of 3 positive squares.
56493² = 8532² + 55845² is the sum of 2 positive squares in 1 way.
56493² is the sum of 3 positive squares.
56493 is a proper divisor of 1033¹² - 1.
56493 is palindromic in (at least) the following bases: 67, and -52.
56493 in base 6 = 1113313 and consists of only the digits '1' and '3'.
56493 in base 48 = OOj and consists of only the digits 'O' and 'j'.
56493 in base 51 = Laa and consists of only the digits 'L' and 'a'.

The number 56493 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A322569: a(n)=x is the least integer such that gcd(sigma(x), sigma(x+1)) = 2*n.

Number of the day: 7335228

Properties of the number 7335228:

7335228 = 2² × 3 × 17 × 41 × 877 is the 6837343^th composite number and is not squarefree.
7335228 has 5 distinct prime factors, 48 divisors, 17 antidivisors and 2242560 totatives.
7335228 has a sphenic digit sum 30 in base 10.
7335228 has an oblong digit sum 30 in base 10.
Reversing the decimal digits of 7335228 results in a semiprime.
7335228 = 1833808² - 1833806² = 611272² - 611266² = 107888² - 107854² = 44768² - 44686² = 36008² - 35906² = 15032² - 14786² = 3328² - 1934² = 2968² - 1214² is the difference of 2 nonnegative squares in 8 ways.
7335228 is the difference of 2 positive pentagonal numbers in 4 ways.
7335228 is not the sum of 3 positive squares.
7335228² = 4571172² + 5736720² = 3451872² + 6472260² = 600240² + 7310628² = 4593372² + 5718960² = 1946940² + 7072128² = 1019172² + 7264080² = 4788420² + 5556672² = 3200400² + 6600228² = 2190372² + 7000560² = 4317660² + 5929872² = 1610172² + 7156320² = 1361700² + 7207728² = 2910672² + 6733020² is the sum of 2 positive squares in 13 ways.
7335228² is the sum of 3 positive squares.
7335228 is a proper divisor of 151⁴⁰ - 1.

Number of the day: 727733159

Properties of the number 727733159:

727733159 is a cyclic number.
727733159 = 109 × 6676451 is semiprime and squarefree.
727733159 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 721056600 totatives.
Reversing the decimal digits of 727733159 results in a sphenic number.
727733159 = 363866580² - 363866579² = 3338280² - 3338171² is the difference of 2 nonnegative squares in 2 ways.
727733159 is the difference of 2 positive pentagonal numbers in 2 ways.
727733159 is not the sum of 3 positive squares.
727733159² = 400587060² + 607557041² is the sum of 2 positive squares in 1 way.
727733159² is the sum of 3 positive squares.
727733159 is a proper divisor of 499¹⁶⁴¹⁷⁵ - 1.
727733159 = '7' + '27733159' is the concatenation of 2 prime numbers.
727733159 is an emirpimes in (at least) the following bases: 2, 4, 5, 8, 9, 14, 19, 25, 28, 32, 35, 40, 42, 48, 51, 54, 56, 57, 59, 63, 64, 69, 71, 80, 81, 86, 90, and 94.

Number of the day: 4826

Norbert Wiener was born on this day 126 years ago.

Properties of the number 4826:

4826 = 2 × 19 × 127 is a sphenic number and squarefree.
4826 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 2268 totatives.
4826 has an oblong digit sum 20 in base 10.
4826 = 1³ + 9³ + 16³ is the sum of 3 positive cubes in 1 way.
4826 = 9² + 16² + 67² is the sum of 3 positive squares.
4826² is the sum of 3 positive squares.
4826 is a proper divisor of 761² - 1.
4826 = '482' + '6' is the concatenation of 2 semiprime numbers.
4826 is palindromic in (at least) base -67.

The number 4826 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003359: Numbers that are the sum of 3 nonzero 6th powers.
A025414: a(n) is the smallest number that is the sum of 3 nonzero squares in exactly n ways.
A051989: Discriminants of real quadratic fields with class number 2 and related continued fraction period length of 24.
A071609: Squared radii of the spheres around (0,0,0) that contain record numbers of lattice points.
A091710: Number of primes less than 10^n having at least one digit 9.
A092265: Sum of smallest parts of all partitions of n into distinct parts.
A095809: Least positive number having exactly n partitions into three squares.
A237859: T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element greater than all horizontal neighbors or less than all vertical neighbors
A278180: Square spiral in which each new term is the sum of its two largest neighbors.
A324703: Lexicographically earliest sequence containing 3 and all positive integers n such that the prime indices of n - 1 already belong to the sequence.

Number of the day: 9699

Properties of the number 9699:

9699 = 3 × 53 × 61 is a sphenic number and squarefree.
9699 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 6240 totatives.
9699 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 9699 results in a semiprime.
9699 = 4850² - 4849² = 1618² - 1615² = 118² - 65² = 110² - 49² is the difference of 2 nonnegative squares in 4 ways.
9699 is the difference of 2 positive pentagonal numbers in 1 way.
9699 = 7² + 25² + 95² is the sum of 3 positive squares.
9699² = 5124² + 8235² = 3555² + 9024² = 6525² + 7176² = 1749² + 9540² is the sum of 2 positive squares in 4 ways.
9699² is the sum of 3 positive squares.
9699 is a proper divisor of 743⁴ - 1.
9699 = '9' + '699' is the concatenation of 2 semiprime numbers.
9699 is palindromic in (at least) base -34.
9699 consists of only the digits '6' and '9'.

The number 9699 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A033572: a(n) = (2*n+1)*(7*n+1).
A059610: Numbers n such that 2^n - 9 is prime.
A062185: Harmonic mean of digits is 8.
A074343: a(1) = 7; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A111494: 3-almost primes with semiprime digits (digits 4, 6, 9 only).
A114615: Starting numbers for which the RATS sequence has eventual period 14.
A178369: Numbers with rounded up arithmetic mean of digits = 9.
A259487: Least positive integer m with prime(m)+2 and prime(prime(m))+2 both prime such that prime(m*n)+2 and prime(prime(m*n))+2 are both prime.
A286444: Number of non-equivalent ways to tile an n X n X n triangular area with two 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-8) of 1 X 1 X 1 tiles.
A292739: Numbers in which 9 outnumbers all other digits together.

Number of the day: 11232020

John Wallis was born on this day 404 years ago.

Happy Fibonacci Day!

Properties of the number 11232020:

11232020 = 2² × 5 × 433 × 1297 is the 10491199^th composite number and is not squarefree.
11232020 has 4 distinct prime factors, 24 divisors, 13 antidivisors and 4478976 totatives.
11232020 has a prime digit sum 11 in base 10.
11232020 = 2808006² - 2808004² = 561606² - 561596² = 6918² - 6052² = 3462² - 868² is the difference of 2 nonnegative squares in 4 ways.
11232020 is the difference of 2 positive pentagonal numbers in 3 ways.
11232020 = 1666² + 2908² = 1502² + 2996² = 596² + 3298² = 412² + 3326² is the sum of 2 positive squares in 4 ways.
11232020 = 20² + 222² + 3344² is the sum of 3 positive squares.
11232020² = 7227636² + 8597648² = 6739212² + 8985616² = 6230004² + 9345872² = 3931216² + 10521588² = 3341072² + 10723596² = 2740624² + 10892532² = 6720012² + 8999984² = 6210036² + 9359152² = 5680908² + 9689456² = 4343020² + 10358400² = 3761300² + 10583520² = 3167980² + 10776000² = 623520² + 11214700² is the sum of 2 positive squares in 13 ways.
11232020² is the sum of 3 positive squares.
11232020 is a proper divisor of 1291²⁴ - 1.

Number of the day: 34443

Émile Michel Hyacinthe Lemoine was born on this day 180 years ago.

Properties of the number 34443:

34443 = 3² × 43 × 89 is the 30763^th composite number and is not squarefree.
34443 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 22176 totatives.
34443 = 17222² - 17221² = 5742² - 5739² = 1918² - 1909² = 422² - 379² = 238² - 149² = 198² - 69² is the difference of 2 nonnegative squares in 6 ways.
34443 is the difference of 2 positive pentagonal numbers in 1 way.
34443 = 7² + 13² + 185² is the sum of 3 positive squares.
34443² = 15093² + 30960² is the sum of 2 positive squares in 1 way.
34443² is the sum of 3 positive squares.
34443 is a proper divisor of 179⁶ - 1.
34443 is a palindrome (in base 10).
34443 is palindromic in (at least) base -36.
34443 consists of only the digits '3' and '4'.
34443 in base 40 = LL3 and consists of only the digits '3' and 'L'.
34443 in base 41 = KK3 and consists of only the digits '3' and 'K'.

The number 34443 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006341: Octal palindromes which are also primes.
A041657: Denominators of continued fraction convergents to sqrt(347).
A077291: Second member of Diophantine pair (m,k) that satisfies 6*(m^2 + m) = k^2 + k: a(n) = k.
A077741: Smallest multiple of n which begins with R(n) and ends in n where R(n) (A004086) is the digit reversal of n. Suitable number of zeros are assumed to the left of the MSD if required.
A082394: Let p = n-th prime of the form 4k+3, take the solution (x,y) to the Pellian equation x^2 - p*y^2 = 1 with x and smallest y >= 1; sequence gives value of y.
A084008: a(n) = T(n) concatenated with reverse(T(n)) divided by 11, where T(n) is the n-th triangular number.
A094625: Expansion of x*(2+22*x+11*x^2)/((x-1)*(1+x)*(10*x^2-1)).
A095294: Number of A095284-primes in range ]2^n,2^(n+1)].
A096025: Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to 6 and (n+7) mod 9 <> 1.
A175760: Numbers n such that d(n + d(n)) = d(n), where d(n) is the sum of the distinct primes dividing n.

Number of the day: 7247

Benoit Mandelbrot was born on this day 96 years ago.

Properties of the number 7247:

7247 is a cyclic number.
7247 is the 927^th prime.
7247 has 9 antidivisors and 7246 totatives.
7247 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 7247 results in a semiprime.
7247 = 3624² - 3623² is the difference of 2 nonnegative squares in 1 way.
7247 is the sum of 2 positive triangular numbers.
7247 is the difference of 2 positive pentagonal numbers in 1 way.
7247 is not the sum of 3 positive squares.
7247² is the sum of 3 positive squares.
7247 is a proper divisor of 2³⁶²³ - 1.
7247 is an emirp in (at least) the following bases: 6, 7, 8, 13, 15, 18, 21, 23, 29, 31, 36, 38, 39, 43, 46, 53, 64, 65, 67, 68, 69, 70, 71, 79, 80, 81, 84, 89, 98, and 99.
7247 is palindromic in (at least) the following bases: -63, and -69.
7247 in base 15 = 2232 and consists of only the digits '2' and '3'.
7247 in base 19 = 1118 and consists of only the digits '1' and '8'.
7247 in base 42 = 44N and consists of only the digits '4' and 'N'.

The number 7247 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A026378: a(n) = number of integer strings s(0),...,s(n) counted by array T in A026374 that have s(n)=1; also a(n) = T(2n-1,n-1).
A045713: Primes with first digit 7.
A066179: Primes p such that (p-1)/2 and (p-3)/4 are also prime.
A073609: a(0) = 2; a(n) for n > 0 is the smallest prime greater than a(n-1) that differs from a(n-1) by a square.
A075421: Trajectory of n under the Reverse and Add! operation carried out in base 4 (presumably) does not reach a palindrome and (presumably) does not join the trajectory of any term m < n.
A104845: Primes from merging of 4 successive digits in decimal expansion of e.
A126791: Binomial matrix applied to A111418.
A141908: Primes congruent to 2 mod 23.
A198778: Primes from merging of 4 successive digits in decimal expansion of Euler-Mascheroni constant A001620.
A238583: Number T(n,k) of equivalence classes of ways of placing k 4 X 4 tiles in an n X 9 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=4, 0<=k<=2*floor(n/4), read by rows.

Number of the day: 5148

Properties of the number 5148:

5148 is the 1294^th totient number.
5148 = 2² × 3² × 11 × 13 is the 4461^th composite number and is not squarefree.
5148 has 4 distinct prime factors, 36 divisors, 19 antidivisors and 1440 totatives.
5148 = 1288² - 1286² = 432² - 426² = 152² - 134² = 128² - 106² = 112² - 86² = 72² - 6² is the difference of 2 nonnegative squares in 6 ways.
5148 is the sum of 2 positive triangular numbers.
5148 is not the sum of 3 positive squares.
5148² = 1980² + 4752² is the sum of 2 positive squares in 1 way.
5148² is the sum of 3 positive squares.
5148 is a proper divisor of 1871² - 1.
5148 is palindromic in (at least) the following bases: 77, 98, -49, and -62.
5148 in base 50 = 22m and consists of only the digits '2' and 'm'.

The number 5148 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006011: a(n) = n^2*(n^2 - 1)/4.
A028723: a(n) = (1/4)*floor(n/2)*floor((n-1)/2)*floor((n-2)/2)*floor((n-3)/2).
A029651: Central elements of the (1,2)-Pascal triangle A029635.
A033991: a(n) = n*(4*n-1).
A045873: a(n) = A006496(n)/2.
A050486: a(n) = binomial(n+6,6)*(2n+7)/7.
A111125: Triangle read by rows: T(k,s) = ((2*k+1)/(2*s+1))*binomial(k+s,2*s), 0 <= s <= k.
A200192: T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing
A213697: T(n,k)=Half the number of (n+1)X(n+1) symmetric 0..k arrays with no 2X2 subblock summing to 2k
A247726: T(n,k)=Number of length n+3 0..k arrays with no disjoint pairs in any consecutive four terms having the same sum

Number of the day: 95868

Properties of the number 95868:

95868 = 2² × 3² × 2663 is the 86629^th composite number and is not squarefree.
95868 has 3 distinct prime factors, 18 divisors, 25 antidivisors and 31944 totatives.
95868 has a triangular digit sum 36 in base 10.
95868 = 23968² - 23966² = 7992² - 7986² = 2672² - 2654² is the difference of 2 nonnegative squares in 3 ways.
95868 is the difference of 2 positive pentagonal numbers in 1 way.
95868 is not the sum of 3 positive squares.
95868² is the sum of 3 positive squares.
95868 is a proper divisor of 37¹¹ - 1.
95868 is palindromic in (at least) the following bases: -37, and -75.
95868 in base 37 = 1X11 and consists of only the digits '1' and 'X'.
95868 in base 58 = SSq and consists of only the digits 'S' and 'q'.

Number of the day: 16585014736

August Ferdinand Möbius was born on this day 230 years ago.

Properties of the number 16585014736:

16585014736 = 2⁴ × 12049 × 86029 is composite and not squarefree.
16585014736 has 3 distinct prime factors, 20 divisors, 51 antidivisors and 8291722752 totatives.
16585014736 has a semiprime digit sum 46 in base 10.
Reversing the decimal digits of 16585014736 results in a sphenic number.
16585014736 = 4146253685² - 4146253683² = 2073126844² - 2073126840² = 1036563425² - 1036563417² = 356165² - 332067² = 196156² - 147960² = 134225² - 37833² is the difference of 2 nonnegative squares in 6 ways.
16585014736 is the sum of 2 positive triangular numbers.
16585014736 is the difference of 2 positive pentagonal numbers in 3 ways.
16585014736 = 78040² + 102444² = 7640² + 128556² is the sum of 2 positive squares in 2 ways.
16585014736 = 144² + 2420² + 128760² is the sum of 3 positive squares.
16585014736² = 9249838080² + 13766016464² = 4404531536² + 15989459520² = 1964335680² + 16468275536² = 10815182400² + 12573565264² is the sum of 2 positive squares in 4 ways.
16585014736² is the sum of 3 positive squares.
16585014736 is a proper divisor of 1301⁶⁷²⁶⁸ - 1.
16585014736 = '1658501473' + '6' is the concatenation of 2 semiprime numbers.

Number of the day: 21478

Properties of the number 21478:

21478 = 2 × 10739 is semiprime and squarefree.
21478 has 2 distinct prime factors, 4 divisors, 25 antidivisors and 10738 totatives.
21478 has a semiprime digit sum 22 in base 10.
21478 has sum of divisors equal to 32220 which is an oblong number.
21478 is the sum of 2 positive triangular numbers.
21478 is the difference of 2 positive pentagonal numbers in 2 ways.
21478 = 21² + 34² + 141² is the sum of 3 positive squares.
21478² is the sum of 3 positive squares.
21478 is a proper divisor of 853⁵⁹ - 1.
21478 = '21' + '478' is the concatenation of 2 semiprime numbers.
21478 is an emirpimes in (at least) the following bases: 2, 8, 11, 13, 14, 16, 17, 18, 20, 21, 24, 26, 28, 30, 31, 35, 37, 39, 40, 41, 43, 46, 50, 51, 53, 55, 59, 63, 64, 69, 74, 76, 82, 84, 89, 92, and 95.
21478 is palindromic in (at least) the following bases: 91, and -61.

The number 21478 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A024588: a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n+1-k), where k = [ (n+1)/2 ], s = (composite numbers).
A092310: Sum of largest parts (counted with multiplicity) of all partitions of n into odd parts.
A116705: Number of permutations of length n which avoid the patterns 1234, 4312.
A187378: Number of 4-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions
A229063: Volume of the Johnson square pyramid (rounded down) with all the edge lengths equal to n.
A304384: a(n) = 168*2^n - 26 (n>=1).

Number of the day: 429

Properties of the number 429:

429 is the 7^th Catalan number.
429 = 3 × 11 × 13 is a sphenic number and squarefree.
429 has 3 distinct prime factors, 8 divisors, 7 antidivisors and 240 totatives.
429 has an emirpimes digit sum 15 in base 10.
429 has a triangular digit sum 15 in base 10.
429 has an oblong digit product 72 in base 10.
429 = 215² - 214² = 73² - 70² = 25² - 14² = 23² - 10² is the difference of 2 nonnegative squares in 4 ways.
429 is the sum of 2 positive triangular numbers.
429 is the difference of 2 positive pentagonal numbers in 1 way.
429 = 2² + 5² + 20² is the sum of 3 positive squares.
429² = 165² + 396² is the sum of 2 positive squares in 1 way.
429² is the sum of 3 positive squares.
429 is a proper divisor of 131² - 1.
429 is palindromic in (at least) the following bases: 32, 38, and -9.
429 in base 8 = 655 and consists of only the digits '5' and '6'.
429 in base 14 = 229 and consists of only the digits '2' and '9'.
429 in base 20 = 119 and consists of only the digits '1' and '9'.

The number 429 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000108: Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!).
A001790: Numerators in expansion of 1/sqrt(1-x).
A007304: Sphenic numbers: products of 3 distinct primes.
A008593: Multiples of 11.
A009766: Catalan's triangle T(n,k) (read by rows): each term is the sum of the entries above and to the left, i.e., T(n,k) = Sum_{j=0..k} T(n-1,j).
A019565: The squarefree numbers ordered lexicographically by their prime factorization (with factors written in decreasing order). a(n) = Product_{k in I} prime(k+1), where I is the set of indices of nonzero binary digits in n = Sum_{k in I} 2^k.
A033184: Catalan triangle A009766 transposed.
A039598: Triangle formed from odd-numbered columns of triangle of expansions of powers of x in terms of Chebyshev polynomials U_n(x). Sometimes called Catalan's triangle.
A039599: Triangle formed from even-numbered columns of triangle of expansions of powers of x in terms of Chebyshev polynomials U_n(x).
A089408: Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A089864.

Number of the day: 483586

Properties of the number 483586:

483586 = 2 × 241793 is semiprime and squarefree.
483586 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 241792 totatives.
483586 has a semiprime digit sum 34 in base 10.
483586 has a Fibonacci digit sum 34 in base 10.
483586 is the difference of 2 positive pentagonal numbers in 2 ways.
483586 = 419² + 555² is the sum of 2 positive squares in 1 way.
483586 = 49² + 96² + 687² is the sum of 3 positive squares.
483586² = 132464² + 465090² is the sum of 2 positive squares in 1 way.
483586² is the sum of 3 positive squares.
483586 is a proper divisor of 163¹⁸⁸⁹ - 1.
483586 = '4835' + '86' is the concatenation of 2 semiprime numbers.
483586 is an emirpimes in (at least) the following bases: 6, 7, 9, 12, 13, 20, 30, 36, 41, 44, 50, 57, 61, 66, 68, 70, 74, 79, 80, 81, 82, 92, 95, 98, and 99.

Number of the day: 596698

Properties of the number 596698:

596698 = 2 × 298349 is semiprime and squarefree.
596698 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 298348 totatives.
596698 has a prime digit sum 43 in base 10.
596698 = 47³ + 59³ + 66³ is the sum of 3 positive cubes in 1 way.
596698 is the sum of 2 positive triangular numbers.
596698 is the difference of 2 positive pentagonal numbers in 2 ways.
596698 = 333² + 697² is the sum of 2 positive squares in 1 way.
596698 = 67² + 228² + 735² is the sum of 3 positive squares.
596698² = 374920² + 464202² is the sum of 2 positive squares in 1 way.
596698² is the sum of 3 positive squares.
596698 is a proper divisor of 13⁷⁴⁵⁸⁷ - 1.
596698 is an emirpimes in (at least) the following bases: 6, 13, 14, 16, 18, 26, 31, 34, 37, 44, 48, 49, 51, 55, 58, 59, 61, 63, 67, 70, 74, 76, 78, 79, 83, 92, 94, and 98.
596698 is palindromic in (at least) the following bases: -21, and -85.

The number 596698 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A185997: Inverse of coefficient array of orthogonal polynomials P(n,x)=(x-2n+2)*P(n-1,x)-(2n-3)*P(n-2,x), P(0,x)=1, P(1,x)=x-1.

Number of the day: 9695

Floris Takens was born on this day 80 years ago.

Properties of the number 9695:

9695 is a cyclic number.
9695 = 5 × 7 × 277 is a sphenic number and squarefree.
9695 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 6624 totatives.
9695 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 9695 results in a semiprime.
9695 = (30 × 31)/2 + … + (43 × 44)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
9695 = 4848² - 4847² = 972² - 967² = 696² - 689² = 156² - 121² is the difference of 2 nonnegative squares in 4 ways.
9695 is the difference of 2 positive pentagonal numbers in 4 ways.
9695 is not the sum of 3 positive squares.
9695² = 5817² + 7756² = 2072² + 9471² = 4641² + 8512² = 4025² + 8820² is the sum of 2 positive squares in 4 ways.
9695² is the sum of 3 positive squares.
9695 is a proper divisor of 991³ - 1.
9695 = '9' + '695' is the concatenation of 2 semiprime numbers.
9695 is palindromic in (at least) base 74.

The number 9695 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006477: Number of partitions of n with at least 1 odd and 1 even part.
A035622: Number of partitions of n into parts 4k and 4k+2 with at least one part of each type.
A047967: Number of partitions of n with some part repeated.
A055831: T(n,n-4), where T is the array in A055830.
A065903: Integers i > 1 for which there is no prime p such that i is a solution mod p of x^4 = 2.
A072895: Least k for the Theodorus spiral to complete n revolutions.
A139273: a(n) = n*(8*n - 3).
A143328: Table T(n,k) read by antidiagonals. T(n,k) is the number of primitive (=aperiodic) k-ary Lyndon words (n,k >= 1) with length less than or equal to n.
A212685: Number of (w,x,y,z) with all terms in {1,...,n} and |w-x|=w+|y-z|.
A215474: Triangle read by rows: number of k-ary n-tuples (a_1,..,a_n) such that the string a_1...a_n is preprime.

Number of the day: 10723493

Properties of the number 10723493:

10723493 is a cyclic number.
10723493 = 11 × 974863 is semiprime and squarefree.
10723493 has 2 distinct prime factors, 4 divisors, 33 antidivisors and 9748620 totatives.
10723493 has a prime digit sum 29 in base 10.
10723493 = 5361747² - 5361746² = 487437² - 487426² is the difference of 2 nonnegative squares in 2 ways.
10723493 is the sum of 2 positive triangular numbers.
10723493 is the difference of 2 positive pentagonal numbers in 2 ways.
10723493 = 90² + 97² + 3272² is the sum of 3 positive squares.
10723493² is the sum of 3 positive squares.
10723493 is a proper divisor of 461¹⁵⁴⁷⁴ - 1.
10723493 = '107234' + '93' is the concatenation of 2 emirpimes.
10723493 is an emirpimes in (at least) the following bases: 2, 3, 7, 9, 13, 14, 17, 18, 21, 24, 43, 45, 48, 53, 54, 71, 73, 79, 81, 88, 95, 98, and 99.

Number of the day: 97538

Properties of the number 97538:

97538 = 2 × 7 × 6967 is a sphenic number and squarefree.
97538 has 3 distinct prime factors, 8 divisors, 37 antidivisors and 41796 totatives.
Reversing the decimal digits of 97538 results in a prime.
97538 = 47² + 48² + 305² is the sum of 3 positive squares.
97538² is the sum of 3 positive squares.
97538 is a proper divisor of 383⁶ - 1.
97538 = '9' + '7538' is the concatenation of 2 semiprime numbers.
97538 is palindromic in (at least) the following bases: 81, -84, and -86.

The number 97538 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A295726: a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = -1, a(2) = 1, a(3) = 1.
A295730: a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = 0, a(2) = 0, a(3) = 1.
A295850: a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = 0, a(2) = 2, a(3) = 1.

Number of the day: 364373

Hermann Weyl was born on this day 135 years ago.

Properties of the number 364373:

364373 is a cyclic number.
364373 is the 31091^th prime.
364373 has 15 antidivisors and 364372 totatives.
364373 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 364373 results in an emirp.
364373 = 182187² - 182186² is the difference of 2 nonnegative squares in 1 way.
364373 is the difference of 2 positive pentagonal numbers in 1 way.
364373 = 242² + 553² is the sum of 2 positive squares in 1 way.
364373 = 23² + 62² + 600² is the sum of 3 positive squares.
364373² = 247245² + 267652² is the sum of 2 positive squares in 1 way.
364373² is the sum of 3 positive squares.
364373 is a proper divisor of 659²⁵⁶⁶ - 1.
364373 = '3' + '64373' is the concatenation of 2 prime numbers.
364373 is an emirp in (at least) the following bases: 2, 10, 14, 16, 21, 22, 34, 46, 53, 60, 63, 70, 76, 78, 81, 83, 86, 91, 92, 94, and 99.

Number of the day: 2616

Felix Hausdorff was born on this day 152 years ago.

Properties of the number 2616:

2616 is the 694^th totient number.
2616 = 2³ × 3 × 109 is the 2236^th composite number and is not squarefree.
2616 has 3 distinct prime factors, 16 divisors, 3 antidivisors and 864 totatives.
2616 has an emirpimes digit sum 15 in base 10.
2616 has a triangular digit sum 15 in base 10.
2616 has an oblong digit product 72 in base 10.
Reversing the decimal digits of 2616 results in an oblong number.
2616 = 655² - 653² = 329² - 325² = 221² - 215² = 115² - 103² is the difference of 2 nonnegative squares in 4 ways.
2616 = 4² + 10² + 50² is the sum of 3 positive squares.
2616² = 1440² + 2184² is the sum of 2 positive squares in 1 way.
2616² is the sum of 3 positive squares.
2616 is a proper divisor of 653² - 1.
2616 in base 25 = 44g and consists of only the digits '4' and 'g'.
2616 in base 29 = 336 and consists of only the digits '3' and '6'.

The number 2616 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A026772: a(n) = T(2n, n-2), T given by A026769.
A064403: Numbers k such that prime(k) + k and prime(k) - k are both primes.
A092049: Numbers n such that prime(n) == -7 (mod n).
A165037: Consider the base-5 Kaprekar map n->K(n) defined in A165032. Sequence gives numbers belonging to cycles, including fixed points.
A165039: Consider the base-5 Kaprekar map n->K(n) defined in A165032. Sequence gives numbers belonging to cycles of length greater than 1
A206038: Values of the difference d for 4 primes in arithmetic progression with the minimal start sequence {5 + j*d}, j = 0 to 3.
A224492: Smallest k such that k*2*p(n)^2-1=q is prime, k*2*q^2-1=r, k*2*r^2-1=s, k*2*r^2-1=t, r, s, and t are also prime.
A254242: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock diagonal sum plus antidiagonal minimum nondecreasing horizontally and vertically
A257426: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock diagonal sum plus antidiagonal minimum nondecreasing horizontally, vertically and ne-to-sw antidiagonally
A326083: Number of subsets of {1..n} containing all of their pairwise sums <= n.

Number of the day: 8322

Properties of the number 8322:

8322 = 2 × 3 × 19 × 73 is the 7277^th composite number and is squarefree.
8322 has 4 distinct prime factors, 16 divisors, 15 antidivisors and 2592 totatives.
8322 has an emirpimes digit sum 15 in base 10.
8322 has a triangular digit sum 15 in base 10.
Reversing the decimal digits of 8322 results in a sphenic number.
8322 is the sum of 2 positive triangular numbers.
8322 = 4² + 5² + 91² is the sum of 3 positive squares.
8322² = 5472² + 6270² is the sum of 2 positive squares in 1 way.
8322² is the sum of 3 positive squares.
8322 is a proper divisor of 1597³ - 1.
8322 is palindromic in (at least) the following bases: 4, 8, 36, 47, 64, -8, -59, -65, and -80.
8322 in base 4 = 2002002 and consists of only the digits '0' and '2'.
8322 in base 8 = 20202 and consists of only the digits '0' and '2'.
8322 in base 21 = ii6 and consists of only the digits '6' and 'i'.
8322 in base 27 = bb6 and consists of only the digits '6' and 'b'.
8322 in base 35 = 6rr and consists of only the digits '6' and 'r'.
8322 in base 36 = 6f6 and consists of only the digits '6' and 'f'.
8322 in base 45 = 44g and consists of only the digits '4' and 'g'.
8322 in base 46 = 3gg and consists of only the digits '3' and 'g'.
8322 in base 47 = 3a3 and consists of only the digits '3' and 'a'.

The number 8322 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A119873: 3*Volume of the root-n Waterman polyhedron as defined in A119870.
A152973: Records in A152968.
A153127: a(n) = (2*n + 1)*(5*n + 6).
A164016: 6 times centered hexagonal numbers: 18*n*(n+1) + 6.
A195904: Base 2 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,0,0,0,0.
A215703: A(n,k) is the n-th derivative of f_k at x=1, and f_k is the k-th of all functions that are representable as x^x^...^x with m>=1 x's and parentheses inserted in all possible ways; square array A(n,k), n>=0, k>=1, read by antidiagonals.
A215704: n-th derivative of ((x^x)^x)^x at x=1.
A259382: Palindromic numbers in bases 4 and 8 written in base 10.
A288952: Number of relaxed compacted binary trees of right height at most one with empty sequences between branch nodes on level 0.
A301932: G.f. A(x) satisfies: A(x) = x*(1 + 3*A(x)*A'(x)) / (1 + A(x)*A'(x)).

Number of the day: 8080525276

Properties of the number 8080525276:

8080525276 = 2² × 19 × 1231 × 86371 is the 7709210041^th composite number and is not squarefree.
8080525276 has 4 distinct prime factors, 24 divisors, 21 antidivisors and 3824463600 totatives.
8080525276 has a prime digit sum 43 in base 10.
8080525276 = 2020131320² - 2020131318² = 106322720² - 106322682² = 1642280² - 1639818² = 109760² - 62982² is the difference of 2 nonnegative squares in 4 ways.
8080525276 is the difference of 2 positive pentagonal numbers in 4 ways.
8080525276 is not the sum of 3 positive squares.
8080525276² is the sum of 3 positive squares.
8080525276 is a proper divisor of 761⁴³¹⁸⁵ - 1.
8080525276 = '808052527' + '6' is the concatenation of 2 semiprime numbers.

Number of the day: 83658

Properties of the number 83658:

83658 = 2 × 3 × 73 × 191 is the 75492^th composite number and is squarefree.
83658 has 4 distinct prime factors, 16 divisors, 13 antidivisors and 27360 totatives.
83658 has a sphenic digit sum 30 in base 10.
83658 has an oblong digit sum 30 in base 10.
83658 is the sum of 2 positive triangular numbers.
83658 is the difference of 2 positive pentagonal numbers in 3 ways.
83658 = 4² + 11² + 289² is the sum of 3 positive squares.
83658² = 55008² + 63030² is the sum of 2 positive squares in 1 way.
83658² is the sum of 3 positive squares.
83658 is a proper divisor of 383¹⁸ - 1.
83658 is palindromic in (at least) base 68.

The number 83658 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A227161: Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of one or less, with rows and columns of the latter in lexicographically nondecreasing order.
A239983: Number of nX5 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4
A239986: T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4
A239990: Number of 6Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4
A298402: a(n) = 2*a(n-1) - a(n-3) + a(floor(n/2)), where a(0) = 1, a(1) = 1, a(2) = 1.

Number of the day: 127505497

Properties of the number 127505497:

127505497 = 7² × 347 × 7499 is the 120260969^th composite number and is not squarefree.
127505497 has 3 distinct prime factors, 12 divisors, 27 antidivisors and 108960936 totatives.
Reversing the decimal digits of 127505497 results in a sphenic number.
127505497 = 63752749² - 63752748² = 9107539² - 9107532² = 1301101² - 1301052² = 183899² - 183552² = 27461² - 25032² = 12251² - 4752² is the difference of 2 nonnegative squares in 6 ways.
127505497 is the sum of 2 positive triangular numbers.
127505497 is the difference of 2 positive pentagonal numbers in 5 ways.
127505497 = 151² + 330² + 11286² is the sum of 3 positive squares.
127505497² is the sum of 3 positive squares.
127505497 is a proper divisor of 211⁵⁵⁷⁰⁶ - 1.

Number of the day: 34120

Martin Wilhelm Kutta was born on this day 153 years ago.

Properties of the number 34120:

34120 is the 7382^th totient number.
34120 = 2³ × 5 × 853 is the 30475^th composite number and is not squarefree.
34120 has 3 distinct prime factors, 16 divisors, 13 antidivisors and 13632 totatives.
34120 has a semiprime digit sum 10 in base 10.
34120 has a triangular digit sum 10 in base 10.
34120 = 1³ + 23³ + 28³ is the sum of 3 positive cubes in 1 way.
34120 = 8531² - 8529² = 4267² - 4263² = 1711² - 1701² = 863² - 843² is the difference of 2 nonnegative squares in 4 ways.
34120 is the sum of 2 positive triangular numbers.
34120 is the difference of 2 positive pentagonal numbers in 2 ways.
34120 = 102² + 154² = 62² + 174² is the sum of 2 positive squares in 2 ways.
34120 = 26² + 120² + 138² is the sum of 3 positive squares.
34120² = 20472² + 27296² = 13312² + 31416² = 21576² + 26432² = 8200² + 33120² is the sum of 2 positive squares in 4 ways.
34120² is the sum of 3 positive squares.
34120 is a proper divisor of 1373⁴ - 1.
34120 is palindromic in (at least) the following bases: 33, 64, and 74.
34120 in base 33 = vav and consists of only the digits 'a' and 'v'.
34120 in base 38 = NNY and consists of only the digits 'N' and 'Y'.

The number 34120 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A047098: a(n) = 2*binomial(3*n, n) - Sum_{k=0..n} binomial(3*n, k).
A051054: a(n) = Sum_{k=1..n} C(n, floor(n/k)).
A107027: Number triangle associated to the Riordan arrays (1/(1+x),x/(1+x)^k),k>=0.
A107030: Number triangle associated with the Riordan arrays (1/(1+x),x/(1+x)^k),k>=0.
A129873: Sequence s_n arising in enumeration of arrays of directed blocks (see Quaintance reference for precise definition).
A192320: Numbers k for which there are no prime numbers in the range (k-4*sqrt(sqrt(k)), k].
A203569: Numbers whose digits are a permutation of [0,...,n] and which contain the product of any two adjacent digits as a substring.
A213028: Number A(n,k) of 3n-length k-ary words that can be built by repeatedly inserting triples of identical letters into the initially empty word; square array A(n,k), n>=0, k>=0, read by antidiagonals.
A252369: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row, column, diagonal and antidiagonal sum not equal to 1 3 4 6 or 7
A330620: Number of length n necklaces with entries covering an initial interval of positive integers and no adjacent entries equal.

Number of the day: 983843

George Boole was born on this day 205 years ago.

Properties of the number 983843:

983843 is a cyclic number.
983843 = 7 × 140549 is semiprime and squarefree.
983843 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 843288 totatives.
983843 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 983843 results in a prime.
983843 = 491922² - 491921² = 70278² - 70271² is the difference of 2 nonnegative squares in 2 ways.
983843 is the difference of 2 positive pentagonal numbers in 2 ways.
983843 = 9² + 41² + 991² is the sum of 3 positive squares.
983843² = 318507² + 930860² is the sum of 2 positive squares in 1 way.
983843² is the sum of 3 positive squares.
983843 is a proper divisor of 1901²⁵⁷¹ - 1.
983843 is an emirpimes in (at least) the following bases: 4, 7, 8, 19, 21, 23, 25, 32, 34, 38, 39, 45, 47, 49, 50, 52, 53, 56, 59, 61, 63, 65, 75, 81, 82, 84, 91, and 98.

Number of the day: 80866668

Properties of the number 80866668:

80866668 = 2² × 3 × 6738889 is the 76149589^th composite number and is not squarefree.
80866668 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 26955552 totatives.
80866668 = 20216668² - 20216666² = 6738892² - 6738886² is the difference of 2 nonnegative squares in 2 ways.
80866668 is the sum of 2 positive triangular numbers.
80866668 is the difference of 2 positive pentagonal numbers in 1 way.
80866668 = 122² + 178² + 8990² is the sum of 3 positive squares.
80866668² = 25781268² + 76646880² is the sum of 2 positive squares in 1 way.
80866668² is the sum of 3 positive squares.
80866668 is a proper divisor of 311⁴³¹⁹⁸ - 1.