Saturday, September 30, 2017

Number of the day: 955738977518

Properties of the number 955738977518:

955738977518 = 2 × 132 × 17 × 2671 × 62273 is composite and not squarefree.
955738977518 has 5 distinct prime factors, 48 divisors, 55 antidivisors and 415000535040 totatives.
955738977518 has a semiprime digit sum 74 in base 10.
Reversing the decimal digits of 955738977518 results in a semiprime.
955738977518 is the difference of 2 positive pentagonal numbers in 11 ways.
955738977518 = 3872 + 27822 + 9776152 is the sum of 3 positive squares.
9557389775182 = 4497595188322 + 8432990978102 = 1427856288822 + 9450128344802 = 4078841364002 + 8643306800182 = 4952685937682 + 8174019899502 = 908168259182 + 9514143667602 = 6409651906322 + 7089433105302 = 6054455061202 + 7395084396182 = 440735566702 + 9547222186322 = 2316643558322 + 9272370890902 = 3189896719182 + 9009342830402 = 2820976863682 + 9131581946702 = 5640369931202 + 7715563903822 = 3265175702402 + 8982334159182 = 2744464519502 + 9154868312322 = 5704736704182 + 7668094838402 = 3675919144302 + 8822205946322 = 2319371397202 + 9271688931182 = 4881694764182 + 8216614603602 = 5706992417102 + 7666416168322 = 6729759664182 + 6786312266402 = 1345943396322 + 9462142235702 = 1425075991502 + 9450548012322 is the sum of 2 positive squares in 22 ways.
9557389775182 is the sum of 3 positive squares.
955738977518 is a proper divisor of 257194376 - 1.
955738977518 = '955' + '738977518' is the concatenation of 2 semiprime numbers.

Friday, September 29, 2017

Number of the day: 976985

Properties of the number 976985:

976985 = 5 × 37 × 5281 is a sphenic number and squarefree.
976985 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 760320 totatives.
Reversing the decimal digits of 976985 results in a semiprime.
976985 = 4884932 - 4884922 = 977012 - 976962 = 132212 - 131842 = 27332 - 25482 is the difference of 2 nonnegative squares in 4 ways.
976985 is the difference of 2 positive pentagonal numbers in 4 ways.
976985 = 6162 + 7732 = 3322 + 9312 = 2932 + 9442 = 292 + 9882 is the sum of 2 positive squares in 4 ways.
976985 = 422 + 552 + 9862 is the sum of 3 positive squares.
9769852 = 6310252 + 7458602 = 3550152 + 9102002 = 406252 + 9761402 = 5531842 + 8052872 = 2621082 + 9411692 = 573042 + 9753032 = 6181842 + 7565372 = 5151512 + 8301322 = 2180732 + 9523362 = 5861912 + 7815882 = 5492242 + 8079932 = 3010172 + 9294562 = 3168602 + 9241752 is the sum of 2 positive squares in 13 ways.
9769852 is the sum of 3 positive squares.
976985 is a proper divisor of 115312 - 1.

Thursday, September 28, 2017

Number of the day: 829888

Properties of the number 829888:

829888 = 26 × 12967 is the 763731th composite number and is not squarefree.
829888 has 2 distinct prime factors, 14 divisors, 25 antidivisors and 414912 totatives.
829888 has a prime digit sum 43 in base 10.
829888 = 2074732 - 2074712 = 1037382 - 1037342 = 518722 - 518642 = 259422 - 259262 = 129832 - 129512 is the difference of 2 nonnegative squares in 5 ways.
829888 is the sum of 2 positive triangular numbers.
829888 is the difference of 2 positive pentagonal numbers in 1 way.
829888 is not the sum of 3 positive squares.
8298882 is the sum of 3 positive squares.
829888 is a proper divisor of 1932161 - 1.

Wednesday, September 27, 2017

Number of the day: 58200

Properties of the number 58200:

58200 = 23 × 3 × 52 × 97 is the 52305th composite number and is not squarefree.
58200 has 4 distinct prime factors, 48 divisors, 19 antidivisors and 15360 totatives.
58200 has an emirpimes digit sum 15 in base 10.
58200 has a triangular digit sum 15 in base 10.
58200 is the difference of 2 nonnegative squares in 12 ways.
58200 is the sum of 2 positive triangular numbers.
58200 is the difference of 2 positive pentagonal numbers in 1 way.
58200 = 202 + 342 + 2382 is the sum of 3 positive squares.
582002 = 390002 + 432002 = 52802 + 579602 = 111602 + 571202 = 305522 + 495362 = 253442 + 523922 = 349202 + 465602 = 162962 + 558722 is the sum of 2 positive squares in 7 ways.
582002 is the sum of 3 positive squares.
58200 is a proper divisor of 1934 - 1.
58200 in base 5 = 3330300 and consists of only the digits '0' and '3'.
58200 in base 22 = 5a5a and consists of only the digits '5' and 'a'.
58200 in base 58 = HHQ and consists of only the digits 'H' and 'Q'.

The number 58200 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A015578: Expansion of x/(1-8x-11x^2).
A018211: Alkane (or paraffin) numbers l(10,n).

Tuesday, September 26, 2017

Number of the day: 5370

Properties of the number 5370:

5370 = 2 × 3 × 5 × 179 is the 4661th composite number and is squarefree.
5370 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 1424 totatives.
5370 has an emirpimes digit sum 15 in base 10.
5370 has a triangular digit sum 15 in base 10.
5370 is the sum of 2 positive triangular numbers.
5370 is the difference of 2 positive pentagonal numbers in 1 way.
5370 is the difference of 2 positive pentagonal pyramidal numbers in 2 ways.
5370 = (60 × (3 × 60-1))/2 is a pentagonal number.
5370 = 42 + 52 + 732 is the sum of 3 positive squares.
53702 = 32222 + 42962 is the sum of 2 positive squares in 1 way.
53702 is the sum of 3 positive squares.
5370 is a proper divisor of 3592 - 1.
5370 is palindromic in (at least) the following bases: 44, 59, -23, -61, and -91.
5370 in base 22 = b22 and consists of only the digits '2' and 'b'.
5370 in base 43 = 2cc and consists of only the digits '2' and 'c'.
5370 in base 44 = 2Y2 and consists of only the digits '2' and 'Y'.
5370 in base 58 = 1YY and consists of only the digits '1' and 'Y'.
5370 in base 59 = 1W1 and consists of only the digits '1' and 'W'.

The number 5370 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002625: Expansion of 1/((1-x)^3*(1-x^2)^2*(1-x^3)).
A014633: Even pentagonal numbers.
A049452: Pentagonal numbers with even index.
A196485: T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,2,1,4 for x=0,1,2,3,4
A222604: Number of nX1 0..3 arrays with exactly floor(nX1/2) elements equal to at least one king-move neighbor, with new values introduced in row major 0..3 order
A222747: T(n,k)=Number of nXk 0..3 arrays with exactly floor(nXk/2) elements equal to at least one horizontal or antidiagonal neighbor, with new values introduced in row major 0..3 order
A226253: Number of ways of writing n as the sum of 9 triangular numbers.
A232696: E.g.f. A(x) satisfies: A'(x) = A(x/A'(x)) with A(0)=1.
A246479: T(n,k)=Number of length n+3 0..k arrays with no pair in any consecutive four terms totalling exactly k
A263373: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with each row and column divisible by 7, read as a base-3 number with top and left being the most significant digits.

Monday, September 25, 2017

Number of the day: 672028146

Properties of the number 672028146:

672028146 = 2 × 32 × 37334897 is the 637149995th composite number and is not squarefree.
672028146 has 3 distinct prime factors, 12 divisors, 7 antidivisors and 224009376 totatives.
672028146 has a triangular digit sum 36 in base 10.
672028146 is the sum of 2 positive triangular numbers.
672028146 is the difference of 2 positive pentagonal numbers in 2 ways.
672028146 = 48752 + 254612 is the sum of 2 positive squares in 1 way.
672028146 = 9292 + 13242 + 258732 is the sum of 3 positive squares.
6720281462 = 2482447502 + 6244968962 is the sum of 2 positive squares in 1 way.
6720281462 is the sum of 3 positive squares.
672028146 is a proper divisor of 1789264162 - 1.
672028146 = '67202' + '8146' is the concatenation of 2 semiprime numbers.

Sunday, September 24, 2017

Number of the day: 3930

Gerolamo Cardano was born on this day 516 years ago.

Properties of the number 3930:

3930 = 2 × 3 × 5 × 131 is the 3384th composite number and is squarefree.
3930 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 1040 totatives.
3930 has an emirpimes digit sum 15 in base 10.
3930 has a triangular digit sum 15 in base 10.
3930 = 262 + … + 302 is the sum of at least 2 consecutive positive squares in 1 way.
3930 is the difference of 2 positive pentagonal numbers in 1 way.
3930 = 72 + 202 + 592 is the sum of 3 positive squares.
39302 = 23582 + 31442 is the sum of 2 positive squares in 1 way.
39302 is the sum of 3 positive squares.
3930 is a proper divisor of 10492 - 1.
3930 is palindromic in (at least) the following bases: 33, and -20.
3930 in base 19 = agg and consists of only the digits 'a' and 'g'.
3930 in base 32 = 3qq and consists of only the digits '3' and 'q'.
3930 in base 33 = 3k3 and consists of only the digits '3' and 'k'.
3930 in base 62 = 11O and consists of only the digits '1' and 'O'.

The number 3930 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A027578: Sums of five consecutive squares: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2.
A075386: Sum of terms of n-th group in A075383.
A076409: Sum of the quadratic residues of prime(n).
A113744: Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 7 multiples of n-1, n-2, ..., 1, for n>=1.
A138989: a(n) = Frobenius number for 3 successive primes = F[p(n),p(n+1),p(n+2)].
A211978: Total number of parts in all partitions of n plus the sum of largest parts of all partitions of n.
A251829: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum not 3 or 6 and every diagonal and antidiagonal sum 3 or 6
A256874: Numbers divisible by prime(d) for each digit d in their base 4 representation, none of which may be zero.
A282035: Sum of quadratic residues of (n-th prime == 3 mod 4).
A284949: Triangle read by rows: T(n,k) = number of reversible string structures of length n using exactly k different symbols.

Saturday, September 23, 2017

Number of the day: 378574

Properties of the number 378574:

378574 = 2 × 72 × 3863 is the 346389th composite number and is not squarefree.
378574 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 162204 totatives.
378574 has a semiprime digit sum 34 in base 10.
378574 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 378574 results in a semiprime.
378574 = (99 × 100)/2 + … + (147 × 148)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
378574 is the difference of 2 positive pentagonal numbers in 6 ways.
378574 = 52 + 182 + 6152 is the sum of 3 positive squares.
3785742 is the sum of 3 positive squares.
378574 is a proper divisor of 4911931 - 1.
378574 = '3785' + '74' is the concatenation of 2 semiprime numbers.

Thursday, September 21, 2017

Number of the day: 1482

Properties of the number 1482:

1482 = 2 × 3 × 13 × 19 is the 1247th composite number and is squarefree.
1482 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 432 totatives.
1482 has an emirpimes digit sum 15 in base 10.
1482 has a triangular digit sum 15 in base 10.
Reversing the decimal digits of 1482 results in a semiprime.
1482 = 42 + … + 162 is the sum of at least 2 consecutive positive squares in 1 way.
1482 is the sum of 2 positive triangular numbers.
1482 = 38 × 39 is an oblong number.
1482 = 72 + 82 + 372 is the sum of 3 positive squares.
14822 = 5702 + 13682 is the sum of 2 positive squares in 1 way.
14822 is the sum of 3 positive squares.
1482 is a proper divisor of 5712 - 1.
1482 = '14' + '82' is the concatenation of 2 semiprime numbers.
1482 is palindromic in (at least) the following bases: 5, 56, 77, and -37.
1482 in base 3 = 2000220 and consists of only the digits '0' and '2'.
1482 in base 14 = 77c and consists of only the digits '7' and 'c'.
1482 in base 38 = 110 and consists of only the digits '0' and '1'.

The number 1482 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002378: Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1).
A002943: a(n) = 2*n*(2*n+1).
A014574: Average of twin prime pairs.
A033537: a(n) = n*(2*n+5).
A045896: Denominator of n/((n+1)(n+2)) = A026741/A045896.
A046386: Products of four distinct primes.
A097024: Numbers in the 5-cycle-attractor if the f[x]=A063919[x] function is iterated; f[x] is the sum of unitary proper divisors.
A124178: Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 is prime.
A170758: G.f.: (1+x)/(1-38*x).
A177905: Numbers n such that n^3 divides 5^(n^2)-1.

Wednesday, September 20, 2017

Number of the day: 129

Properties of the number 129:

129 = 3 × 43 is semiprime and squarefree.
129 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 84 totatives.
129 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 129 results in an emirpimes.
129 = 13 + 43 + 43 is the sum of 3 positive cubes in 1 way.
129 = 652 - 642 = 232 - 202 is the difference of 2 nonnegative squares in 2 ways.
129 is the difference of 2 positive pentagonal numbers in 1 way.
129 = 22 + 52 + 102 is the sum of 3 positive squares.
1292 is the sum of 3 positive squares.
129 is a proper divisor of 1732 - 1.
129 is an emirpimes in (at least) the following bases: 3, 5, 7, 9, 10, 12, 14, 15, 17, 19, 21, 23, 24, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 45, 51, 55, 60, 69, 71, 72, 78, 80, 84, 89, 91, 93, 94, 98, and 100.
129 is palindromic in (at least) the following bases: 2, 6, 42, -7, -16, -32, and -64.
129 in base 6 = 333 and consists of only the digit '3'.

The number 129 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000051: a(n) = 2^n + 1.
A000930: Narayana's cows sequence: a(0) = a(1) = a(2) = 1; thereafter a(n) = a(n-1) + a(n-3).
A000959: Lucky numbers.
A001358: Semiprimes (or biprimes): products of two primes.
A001969: Evil numbers: numbers with an even number of 1's in their binary expansion.
A005408: The odd numbers: a(n) = 2*n + 1.
A006881: Squarefree semiprimes: Numbers that are the product of two distinct primes.
A007504: Sum of first n primes.
A008585: a(n) = 3*n.
A016813: a(n) = 4n + 1.

Tuesday, September 19, 2017

Number of the day: 962716

Ky Fan was born on this day 103 years ago.

Properties of the number 962716:

962716 = 22 × 229 × 1051 is the 886891th composite number and is not squarefree.
962716 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 478800 totatives.
962716 has an emirp digit sum 31 in base 10.
962716 has sum of divisors equal to 1693720 which is a triangular number.
Reversing the decimal digits of 962716 results in a prime.
962716 = 2406802 - 2406782 = 12802 - 8222 is the difference of 2 nonnegative squares in 2 ways.
962716 is the difference of 2 positive pentagonal numbers in 2 ways.
962716 is not the sum of 3 positive squares.
9627162 = 2522402 + 9290842 is the sum of 2 positive squares in 1 way.
9627162 is the sum of 3 positive squares.
962716 is a proper divisor of 137370 - 1.

Monday, September 18, 2017

Number of the day: 19499565

Adrien-Marie Legendre was born on this day 265 years ago.

Properties of the number 19499565:

19499565 = 3 × 5 × 61 × 101 × 211 is the 18258760th composite number and is squarefree.
19499565 has 5 distinct prime factors, 32 divisors, 35 antidivisors and 10080000 totatives.
19499565 is the difference of 2 nonnegative squares in 16 ways.
19499565 is the difference of 2 positive pentagonal numbers in 7 ways.
19499565 = 1002 + 2772 + 44062 is the sum of 3 positive squares.
194995652 = 83790212 + 176075282 = 50665322 + 188298512 = 114167882 + 158079092 = 38613002 + 191134352 = 3513152 + 194964002 = 72446852 + 181038002 = 129739682 + 145571012 = 101362292 + 166580282 = 119788922 + 153863312 = 116997392 + 155996522 = 86948882 + 174537092 = 132341312 + 143209922 = 35163152 + 191799002 is the sum of 2 positive squares in 13 ways.
194995652 is the sum of 3 positive squares.
19499565 is a proper divisor of 10760 - 1.
19499565 = '194' + '99565' is the concatenation of 2 semiprime numbers.

Sunday, September 17, 2017

Number of the day: 85501

Bernhard Riemann was born on this day 191 years ago.

Properties of the number 85501:

85501 is a cyclic number.
85501 = 13 × 6577 is semiprime and squarefree.
85501 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 78912 totatives.
85501 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 85501 results in an emirpimes.
85501 = 427512 - 427502 = 32952 - 32822 is the difference of 2 nonnegative squares in 2 ways.
85501 is the sum of 2 positive triangular numbers.
85501 is the difference of 2 positive pentagonal numbers in 2 ways.
85501 = 1742 + 2352 = 1502 + 2512 is the sum of 2 positive squares in 2 ways.
85501 = 212 + 462 + 2882 is the sum of 3 positive squares.
855012 = 249492 + 817802 = 84242 + 850852 = 405012 + 753002 = 328852 + 789242 is the sum of 2 positive squares in 4 ways.
855012 is the sum of 3 positive squares.
85501 is a proper divisor of 35312 - 1.
85501 = '85' + '501' is the concatenation of 2 semiprime numbers.
85501 is an emirpimes in (at least) the following bases: 2, 8, 9, 10, 13, 21, 27, 28, 31, 35, 36, 37, 38, 39, 40, 42, 44, 45, 49, 53, 54, 58, 66, 71, 78, 80, 81, 83, 85, 86, 87, 88, 89, and 97.
85501 is palindromic in (at least) the following bases: -14, and -71.
85501 in base 14 = 23233 and consists of only the digits '2' and '3'.

Saturday, September 16, 2017

Number of the day: 11292

Properties of the number 11292:

11292 = 22 × 3 × 941 is the 9926th composite number and is not squarefree.
11292 has 3 distinct prime factors, 12 divisors, 7 antidivisors and 3760 totatives.
11292 has an emirpimes digit sum 15 in base 10.
11292 has a triangular digit sum 15 in base 10.
11292 has a triangular digit product 36 in base 10.
11292 = 342 + … + 412 is the sum of at least 2 consecutive positive squares in 1 way.
11292 = 28242 - 28222 = 9442 - 9382 is the difference of 2 nonnegative squares in 2 ways.
11292 is the sum of 2 positive triangular numbers.
11292 is the difference of 2 positive pentagonal numbers in 1 way.
11292 is not the sum of 3 positive squares.
112922 = 69602 + 88922 is the sum of 2 positive squares in 1 way.
112922 is the sum of 3 positive squares.
11292 is a proper divisor of 974 - 1.
11292 = '1129' + '2' is the concatenation of 2 prime numbers.
11292 is palindromic in (at least) the following bases: 30, -23, and -71.
11292 in base 30 = cgc and consists of only the digits 'c' and 'g'.
11292 in base 47 = 55C and consists of only the digits '5' and 'C'.

The number 11292 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006550: n+8*C(n,2)+30*C(n,3)+62*C(n,4)+75*C(n,5)+30*C(n,6).
A034997: Number of Generalized Retarded Functions in Quantum Field Theory.
A101713: Indices of primes in sequence defined by A(0) = 43, A(n) = 10*A(n-1) - 27 for n > 0.
A137200: Number of ways to tile an n X 1 strip with 1 X 1 squares and 2 X 1 dominoes with the restriction that no three consecutive tiles are of the same type.
A212584: Nonnegative walks of length n on the x-axis starting at the origin using steps {1,-1} and visiting no point more than twice.
A213754: Principal diagonal of the convolution array A213753.
A227333: T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having two adjacent 1s and two adjacent 0s, with rows and columns of the latter in lexicographically nondecreasing order
A271580: Magic sums of 4 X 4 magic squares composed of squares.
A289191: Number of polygonal tiles with n sides with two exits per side and n edges connecting pairs of exits, with no edges between exits on the same side and non-isomorphic under rotational symmetry.
A289343: a(n) = A289191(prime(n)).

Friday, September 15, 2017

Number of the day: 894518

Properties of the number 894518:

894518 = 2 × 447259 is semiprime and squarefree.
894518 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 447258 totatives.
894518 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 894518 results in a sphenic number.
894518 = 72 + 382 + 9452 is the sum of 3 positive squares.
8945182 is the sum of 3 positive squares.
894518 is a proper divisor of 853926 - 1.
894518 = '894' + '518' is the concatenation of 2 sphenic numbers.
894518 is an emirpimes in (at least) the following bases: 2, 7, 8, 16, 26, 27, 30, 32, 36, 38, 40, 41, 43, 52, 62, 67, 70, 75, 76, 82, 84, 87, 88, 90, 91, 98, 99, and 100.

Thursday, September 14, 2017

Number of the day: 8347

Properties of the number 8347:

8347 is a cyclic number.
8347 = 17 × 491 is semiprime and squarefree.
8347 has 2 distinct prime factors, 4 divisors, 25 antidivisors and 7840 totatives.
8347 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 8347 results in an emirpimes.
8347 = 41742 - 41732 = 2542 - 2372 is the difference of 2 nonnegative squares in 2 ways.
8347 is the sum of 2 positive triangular numbers.
8347 is the difference of 2 positive pentagonal numbers in 2 ways.
8347 = 72 + 272 + 872 is the sum of 3 positive squares.
83472 = 39282 + 73652 is the sum of 2 positive squares in 1 way.
83472 is the sum of 3 positive squares.
8347 is a proper divisor of 10110 - 1.
8347 = '83' + '47' is the concatenation of 2 prime numbers.
8347 is an emirpimes in (at least) the following bases: 5, 6, 8, 9, 10, 21, 26, 28, 33, 34, 35, 37, 38, 43, 45, 50, 54, 55, 56, 57, 59, 60, 62, 66, 68, 70, 73, 79, 82, 84, 88, 90, 98, and 99.
8347 is palindromic in (at least) the following bases: 31, 78, -43, and -56.
8347 in base 7 = 33223 and consists of only the digits '2' and '3'.
8347 in base 31 = 8l8 and consists of only the digits '8' and 'l'.
8347 in base 34 = 77h and consists of only the digits '7' and 'h'.

The number 8347 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005676: Sum C(n-k,4*k), k = 0..n.
A007042: Diagonal of partition triangle A047812.
A009962: Coordination sequence for sigma-CrFe, Position Xa.
A031899: Lucky numbers with size of gaps equal to 16 (upper terms).
A035107: First differences give (essentially) A028242.
A128034: a(0)=a(1)=1. a(n) = the multiple of n which is > a(n-1)+a(n-2) and is <= a(n-1)+a(n-2)+n.
A240012: Number of partitions of n, where the difference between the number of odd parts and the number of even parts is 3.
A268325: Number of length-(n+1) 0..6 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.
A272223: Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 441", based on the 5-celled von Neumann neighborhood.
A279754: Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 197", based on the 5-celled von Neumann neighborhood.

Wednesday, September 13, 2017

Number of the day: 4057

Properties of the number 4057:

4057 is a cyclic number.
4057 is the 560th prime.
4057 has 13 antidivisors and 4056 totatives.
4057 has sum of divisors equal to 4058 which is semiprime.
4057 = 20292 - 20282 is the difference of 2 nonnegative squares in 1 way.
4057 is the sum of 2 positive triangular numbers.
4057 is the difference of 2 positive pentagonal numbers in 1 way.
4057 = 242 + 592 is the sum of 2 positive squares in 1 way.
4057 = 42 + 212 + 602 is the sum of 3 positive squares.
40572 = 28322 + 29052 is the sum of 2 positive squares in 1 way.
40572 is the sum of 3 positive squares.
4057 is a proper divisor of 14096 - 1.
4057 is an emirp in (at least) the following bases: 4, 7, 9, 13, 15, 19, 23, 24, 28, 34, 43, 45, 49, 50, 51, 57, 59, 61, 63, 64, 67, 68, 69, 73, 77, 81, 87, 89, 93, 94, 98, and 99.
4057 is palindromic in (at least) the following bases: 52, -12, -22, -25, and -78.
4057 in base 5 = 112212 and consists of only the digits '1' and '2'.
4057 in base 21 = 944 and consists of only the digits '4' and '9'.
4057 in base 22 = 889 and consists of only the digits '8' and '9'.
4057 in base 24 = 711 and consists of only the digits '1' and '7'.
4057 in base 51 = 1SS and consists of only the digits '1' and 'S'.
4057 in base 52 = 1Q1 and consists of only the digits '1' and 'Q'.

The number 4057 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A025019: Smallest prime in Goldbach partition of A025018(n).
A031934: Lower prime of a pair of consecutive primes having a difference of 16.
A045710: Primes with first digit 4.
A059245: Primes p such that x^13 = 2 has no solution mod p.
A098182: a(n) = 3*a(n-1) - a(n-2) + a(n-3), a(0)=1,a(1)=1,a(2)=3.
A104803: "Floor of hypotenuses": a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=1, a(2)=3.
A136065: Mother primes of order 6.
A200838: T(n,k)=Number of 0..k arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases
A212729: T(n,k)=Number of 0..2 arrays of length n+2*k-1 with sum less than 2*k in any length 2k subsequence (=less than 50% duty cycle)
A216451: Numbers which are simultaneously of the form x^2+y^2, x^2+2y^2, x^2+3y^2, x^2+7y^2, all with x>0, y>0.

Tuesday, September 12, 2017

Number of the day: 5382

Properties of the number 5382:

5382 = 2 × 32 × 13 × 23 is the 4672th composite number and is not squarefree.
5382 has 4 distinct prime factors, 24 divisors, 15 antidivisors and 1584 totatives.
5382 has an oblong digit product 240 in base 10.
5382 = 142 + … + 262 is the sum of at least 2 consecutive positive squares in 1 way.
5382 is the sum of 2 positive triangular numbers.
5382 is the difference of 2 positive pentagonal numbers in 2 ways.
5382 = 22 + 72 + 732 is the sum of 3 positive squares.
53822 = 20702 + 49682 is the sum of 2 positive squares in 1 way.
53822 is the sum of 3 positive squares.
5382 is a proper divisor of 1393 - 1.
5382 is palindromic in (at least) the following bases: 28, 77, -4, and -32.
5382 in base 17 = 11aa and consists of only the digits '1' and 'a'.
5382 in base 28 = 6o6 and consists of only the digits '6' and 'o'.

The number 5382 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A055102: Expansion of cube of continued fraction 1/ ( 1+q/ ( 1+q^2/ ( 1+q^3/ ( 1+q^4/... )))).
A077285: Number of partitions of n with designated summands.
A086113: Number of 3 X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing.
A113744: Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 7 multiples of n-1, n-2, ..., 1, for n>=1.
A113746: Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 9 multiples of n-1, n-2, ..., 1, for n>=1.
A134602: Composite numbers such that the square mean of their prime factors is a nonprime integer (where the prime factors are taken with multiplicity and the square mean of c and d is sqrt((c^2+d^2)/2)).
A139274: a(n) = n*(8*n-1).
A152759: 3 times 9-gonal (or nonagonal) numbers: 3n(7n-5)/2.
A182205: Iterate the map in A006368 starting at 40.
A186029: a(n) = n*(7*n+3)/2.

Monday, September 11, 2017

Number of the day: 573272362

Properties of the number 573272362:

573272362 = 2 × 13 × 1559 × 14143 is the 543271742th composite number and is squarefree.
573272362 has 4 distinct prime factors, 16 divisors, 53 antidivisors and 264398832 totatives.
573272362 has an emirp digit sum 37 in base 10.
573272362 is the difference of 2 positive pentagonal numbers in 5 ways.
573272362 = 482 + 532 + 239432 is the sum of 3 positive squares.
5732723622 = 2204893702 + 5291744882 is the sum of 2 positive squares in 1 way.
5732723622 is the sum of 3 positive squares.
573272362 is a proper divisor of 124996637 - 1.
573272362 = '57' + '3272362' is the concatenation of 2 semiprime numbers.

Sunday, September 10, 2017

Number of the day: 239515396887

Properties of the number 239515396887:

239515396887 = 3 × 13 × 43 × 142823731 is composite and squarefree.
239515396887 has 4 distinct prime factors, 16 divisors, 25 antidivisors and 143966319840 totatives.
239515396887 has a sphenic digit sum 66 in base 10.
239515396887 has a triangular digit sum 66 in base 10.
239515396887 = 1197576984442 - 1197576984432 = 399192328162 - 399192328132 = 92121306562 - 92121306432 = 30707102362 - 30707101972 = 27850627762 - 27850627332 = 9283543162 - 9283541872 = 2142358762 - 2142353172 = 714127042 - 714110272 is the difference of 2 nonnegative squares in 8 ways.
239515396887 is the difference of 2 positive pentagonal numbers in 4 ways.
239515396887 is not the sum of 3 positive squares.
2395153968872 = 921213064952 + 2210911355882 is the sum of 2 positive squares in 1 way.
2395153968872 is the sum of 3 positive squares.
239515396887 is a proper divisor of 10972720452 - 1.
239515396887 = '239' + '515396887' is the concatenation of 2 prime numbers.
239515396887 = '23951' + '5396887' is the concatenation of 2 semiprime numbers.

Saturday, September 9, 2017

Number of the day: 2758

Properties of the number 2758:

2758 = 2 × 7 × 197 is a sphenic number and squarefree.
2758 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 1176 totatives.
2758 has a semiprime digit sum 22 in base 10.
2758 is the difference of 2 positive pentagonal numbers in 4 ways.
2758 = 62 + 112 + 512 is the sum of 3 positive squares.
27582 = 3922 + 27302 is the sum of 2 positive squares in 1 way.
27582 is the sum of 3 positive squares.
2758 is a proper divisor of 2114 - 1.
2758 is palindromic in (at least) the following bases: 29, -15, -21, -27, and -52.
2758 in base 14 = 1010 and consists of only the digits '0' and '1'.
2758 in base 17 = 994 and consists of only the digits '4' and '9'.
2758 in base 26 = 422 and consists of only the digits '2' and '4'.
2758 in base 28 = 3ee and consists of only the digits '3' and 'e'.
2758 in base 29 = 383 and consists of only the digits '3' and '8'.
2758 in base 52 = 112 and consists of only the digits '1' and '2'.

The number 2758 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A022265: a(n) = n*(7*n + 1)/2.
A034262: a(n) = n^3 + n.
A052284: Number of compositions of n into nonprime numbers.
A177915: Numbers n such that n^3 divides 15^(n^2)-1.
A182714: Number of 4's in the last section of the set of partitions of n.
A200809: T(n,k)=Number of nXk 0..2 arrays with no average of any element and its diagonal, antidiagonal, horizontal and vertical neighbors equal to one
A227631: Array t(n,k): row n consists of the positive integers m for which the least splitter of H(m) and H(m+1) is n, where H denotes harmonic number.
A229308: Primitive numbers in A229304.
A229309: Primitive numbers in A229305.
A261380: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00001011 00010101 or 01010101.

Friday, September 8, 2017

Number of the day: 853002

Marin Mersenne was born on this day 429 years ago.

Properties of the number 853002:

853002 = 2 × 32 × 47389 is the 785163th composite number and is not squarefree.
853002 has 3 distinct prime factors, 12 divisors, 21 antidivisors and 284328 totatives.
853002 is the sum of 2 positive triangular numbers.
853002 = 692 + 9212 is the sum of 2 positive squares in 1 way.
853002 = 522 + 972 + 9172 is the sum of 3 positive squares.
8530022 = 1270982 + 8434802 is the sum of 2 positive squares in 1 way.
8530022 is the sum of 3 positive squares.
853002 is a proper divisor of 80922 - 1.

Thursday, September 7, 2017

Number of the day: 3641

Properties of the number 3641:

3641 = 11 × 331 is semiprime and squarefree.
3641 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 3300 totatives.
3641 has a semiprime digit sum 14 in base 10.
3641 has an oblong digit product 72 in base 10.
Reversing the decimal digits of 3641 results in a sphenic number.
3641 = 18212 - 18202 = 1712 - 1602 is the difference of 2 nonnegative squares in 2 ways.
3641 is the difference of 2 positive pentagonal numbers in 2 ways.
3641 = 42 + 52 + 602 is the sum of 3 positive squares.
36412 is the sum of 3 positive squares.
3641 is a proper divisor of 6612 - 1.
3641 = '3' + '641' is the concatenation of 2 prime numbers.
3641 is an emirpimes in (at least) the following bases: 4, 6, 7, 9, 14, 18, 23, 27, 30, 31, 32, 40, 42, 44, 45, 46, 47, 49, 50, 55, 57, 59, 60, 63, 65, 66, 68, 70, 74, 81, 83, 84, 85, 89, 92, 95, and 98.
3641 is palindromic in (at least) the following bases: 21, 34, 52, 56, -2, -8, -23, -65, -70, and -91.
3641 in base 3 = 11222212 and consists of only the digits '1' and '2'.
3641 in base 21 = 858 and consists of only the digits '5' and '8'.
3641 in base 22 = 7bb and consists of only the digits '7' and 'b'.
3641 in base 33 = 3bb and consists of only the digits '3' and 'b'.
3641 in base 34 = 353 and consists of only the digits '3' and '5'.
3641 in base 42 = 22T and consists of only the digits '2' and 'T'.
3641 in base 51 = 1KK and consists of only the digits '1' and 'K'.
3641 in base 52 = 1I1 and consists of only the digits '1' and 'I'.
3641 in base 55 = 1BB and consists of only the digits '1' and 'B'.
3641 in base 56 = 191 and consists of only the digits '1' and '9'.

The number 3641 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001701: Generalized Stirling numbers.
A005915: Hexagonal prism numbers: a(n) = (n + 1)*(3*n^2 + 3*n + 1).
A006322: 4-dimensional analog of centered polygonal numbers.
A015565: a(n) = 7*a(n-1) + 8*a(n-2), a(0) = 0, a(1) = 1.
A046063: Numbers n such that n-th partition number A000041(n) is prime.
A056106: Second spoke of a hexagonal spiral.
A060884: a(n) = n^4 - n^3 + n^2 - n + 1.
A113405: Expansion of x^3/(1-2*x+x^3-2*x^4) = x^3/( (1-2*x)*(1+x)*(1-x+x^2) ).
A116520: a(0) = 0, a(1) = 1; a(n) = max { 4*a(k)+a(n-k) | 1 <= k <= n/2 }, for n>1.
A194270: D-toothpick sequence of the second kind (see Comments lines for definition).

Wednesday, September 6, 2017

Number of the day: 5304

Properties of the number 5304:

5304 = 23 × 3 × 13 × 17 is the 4600th composite number and is not squarefree.
5304 has 4 distinct prime factors, 32 divisors, 8 antidivisors and 1536 totatives.
5304 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 5304 results in a sphenic number.
5304 = (16 × 17)/2 + … + (32 × 33)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
5304 = 13272 - 13252 = 6652 - 6612 = 4452 - 4392 = 2272 - 2152 = 1152 - 892 = 952 - 612 = 772 - 252 = 732 - 52 is the difference of 2 nonnegative squares in 8 ways.
5304 is the sum of 2 positive triangular numbers.
5304 is the difference of 2 positive pentagonal numbers in 3 ways.
5304 = 22 + 202 + 702 is the sum of 3 positive squares.
53042 = 24962 + 46802 = 5042 + 52802 = 33602 + 41042 = 20402 + 48962 is the sum of 2 positive squares in 4 ways.
53042 is the sum of 3 positive squares.
5304 is a proper divisor of 1032 - 1.
5304 is palindromic in (at least) the following bases: 21, 77, and -21.
5304 in base 21 = c0c and consists of only the digits '0' and 'c'.
5304 in base 27 = 77c and consists of only the digits '7' and 'c'.
5304 in base 32 = 55o and consists of only the digits '5' and 'o'.
5304 in base 51 = 220 and consists of only the digits '0' and '2'.

The number 5304 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002421: Expansion of (1-4x)^(3/2) in powers of x.
A022264: a(n) = n*(7*n - 1)/2.
A032279: Number of bracelets (turn over necklaces) of n beads of 2 colors, 5 of them black.
A084921: LCM(p-1, p+1) where p is the n-th prime.
A085250: 4 times hexagonal numbers: a(n) = 4*n*(2*n-1).
A188992: T(n,k)=Number of nXk binary arrays without the pattern 0 0 1 antidiagonally or horizontally
A225310: T(n,k)=Number of nXk -1,1 arrays such that the sum over i=1..n,j=1..k of i*x(i,j) is zero and rows are nondecreasing (ways to put k thrusters pointing east or west at each of n positions 1..n distance from the hinge of a south-pointing gate without turning the gate)
A241435: T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4
A252615: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 3 5 6 or 8 and every 3X3 column and antidiagonal sum not equal to 0 3 5 6 or 8
A275090: T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (0,-2) (-1,-2) or (-2,-1) and new values introduced in order 0..2.

Friday, September 1, 2017

Number of the day: 64844

Properties of the number 64844:

64844 = 22 × 13 × 29 × 43 is the 58364th composite number and is not squarefree.
64844 has 4 distinct prime factors, 24 divisors, 19 antidivisors and 28224 totatives.
64844 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 64844 results in a sphenic number.
64844 = (32 × 33)/2 + … + (74 × 75)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
64844 = 162122 - 162102 = 12602 - 12342 = 5882 - 5302 = 4202 - 3342 is the difference of 2 nonnegative squares in 4 ways.
64844 is the difference of 2 positive pentagonal numbers in 3 ways.
64844 = 22 + 182 + 2542 is the sum of 3 positive squares.
648442 = 261442 + 593402 = 249402 + 598562 = 232202 + 605442 = 447202 + 469562 is the sum of 2 positive squares in 4 ways.
648442 is the sum of 3 positive squares.
64844 is a proper divisor of 1736 - 1.
64844 is palindromic in (at least) the following bases: 46, 77, and -63.
64844 in base 41 = cNN and consists of only the digits 'N' and 'c'.
64844 in base 46 = UTU and consists of only the digits 'T' and 'U'.

The number 64844 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A209489: Number of partitions of 1 into rational parts a/b satisfying 0<a<b<=n.