Number of the day: 790843

Properties of the number 790843:

790843 is a cyclic number.
790843 is the 63272^th prime.
790843 has 29 antidivisors and 790842 totatives.
790843 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 790843 results in an emirp.
790843 = 395422² - 395421² is the difference of 2 nonnegative squares in 1 way.
790843 is the sum of 2 positive triangular numbers.
790843 is the difference of 2 positive pentagonal numbers in 1 way.
790843 = 123² + 155² + 867² is the sum of 3 positive squares.
790843² is the sum of 3 positive squares.
790843 is a proper divisor of 1913³⁹ - 1.
790843 is an emirp in (at least) the following bases: 5, 8, 10, 11, 19, 21, 23, 26, 28, 29, 30, 31, 41, 44, 54, 61, 64, 67, 76, 85, 86, 89, 94, 97, 99, and 100.

Number of the day: 7222017

Happy Casual π Day!

Properties of the number 7222017:

7222017 is a cyclic number.
7222017 = 3 × 11 × 218849 is a sphenic number and squarefree.
7222017 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 4376960 totatives.
7222017 has a semiprime digit sum 21 in base 10.
7222017 has a Fibonacci digit sum 21 in base 10.
7222017 has a triangular digit sum 21 in base 10.
7222017 = 3611009² - 3611008² = 1203671² - 1203668² = 328279² - 328268² = 109441² - 109408² is the difference of 2 nonnegative squares in 4 ways.
7222017 is the difference of 2 positive pentagonal numbers in 2 ways.
7222017 = 53² + 218² + 2678² is the sum of 3 positive squares.
7222017² = 3016200² + 6562017² is the sum of 2 positive squares in 1 way.
7222017² is the sum of 3 positive squares.
7222017 is a proper divisor of 397⁶⁸³⁹ - 1.

Number of the day: 1844

Properties of the number 1844:

1844 = 2² × 461 is the 1561^th composite number and is not squarefree.
1844 has 2 distinct prime factors, 6 divisors, 9 antidivisors and 920 totatives.
1844 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 1844 results in a prime.
1844 = 1³ + 8³ + 11³ is the sum of 3 positive cubes in 1 way.
1844 = 462² - 460² is the difference of 2 nonnegative squares in 1 way.
1844 is the difference of 2 positive pentagonal numbers in 1 way.
1844 = 20² + 38² is the sum of 2 positive squares in 1 way.
1844 = 10² + 12² + 40² is the sum of 3 positive squares.
1844² = 1044² + 1520² is the sum of 2 positive squares in 1 way.
1844² is the sum of 3 positive squares.
1844 is a proper divisor of 509⁴ - 1.
1844 is palindromic in (at least) the following bases: 20, -13, -14, -23, and -97.
1844 in base 13 = abb and consists of only the digits 'a' and 'b'.
1844 in base 17 = 668 and consists of only the digits '6' and '8'.
1844 in base 20 = 4c4 and consists of only the digits '4' and 'c'.
1844 in base 42 = 11c and consists of only the digits '1' and 'c'.

The number 1844 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A014561: Numbers n giving rise to prime quadruples (30n+11, 30n+13, 30n+17, 30n+19).
A024026: a(n) = 3^n - n^3.
A067979: Triangle read by rows of incomplete convolutions of Lucas numbers L(n+1) = A000204(n+1), n>=0.
A067990: Triangle A067979 with rows read backwards.
A118551: a(0)=1. a(n) = a(n-1)*2, if n is in the sequence. a(n) = a(n-1) + 1 if n is missing from the sequence.
A134619: Numbers such that the arithmetic mean of the cubes of their prime factors (taken with multiplicity) is a prime.
A138920: Indices k such that A020509(k)=Phi[k](-10) is prime, where Phi is a cyclotomic polynomial.
A138940: Indices n such that A019328(n) = Phi(n,10) is prime, where Phi is a cyclotomic polynomial.
A181470: Numbers n such that 97 is the largest prime factor of n^2-1.
A265067: Coordination sequence for (2,5,8) tiling of hyperbolic plane.

Number of the day: 6052

Properties of the number 6052:

6052 = 2² × 17 × 89 is the 5262^th composite number and is not squarefree.
6052 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 2816 totatives.
6052 has an emirp digit sum 13 in base 10.
6052 has a Fibonacci digit sum 13 in base 10.
Reversing the decimal digits of 6052 results in a sphenic number.
6052 = (53 × 54)/2 + … + (56 × 57)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6052 = 1514² - 1512² = 106² - 72² is the difference of 2 nonnegative squares in 2 ways.
6052 is the difference of 2 positive pentagonal numbers in 1 way.
6052 = 54² + 56² = 24² + 74² is the sum of 2 positive squares in 2 ways.
6052 = 34² + 36² + 60² is the sum of 3 positive squares.
6052² = 2848² + 5340² = 220² + 6048² = 3552² + 4900² = 2652² + 5440² is the sum of 2 positive squares in 4 ways.
6052² is the sum of 3 positive squares.
6052 is a proper divisor of 1123⁴ - 1.
6052 is palindromic in (at least) the following bases: 36, 50, 55, 88, -31, -42, and -55.
6052 in base 6 = 44004 and consists of only the digits '0' and '4'.
6052 in base 27 = 884 and consists of only the digits '4' and '8'.
6052 in base 35 = 4ww and consists of only the digits '4' and 'w'.
6052 in base 36 = 4o4 and consists of only the digits '4' and 'o'.
6052 in base 49 = 2PP and consists of only the digits '2' and 'P'.
6052 in base 50 = 2L2 and consists of only the digits '2' and 'L'.
6052 in base 54 = 244 and consists of only the digits '2' and '4'.
6052 in base 55 = 202 and consists of only the digits '0' and '2'.

The number 6052 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006128: Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n.
A018813: Number of lines through exactly 6 points of an n X n grid of points.
A028305: Triangle of numbers of permutations eliminating just k cards out of n in game of Mousetrap.
A101709: Number of partitions of n having nonnegative even rank (the rank of a partition is the largest part minus the number of parts).
A108099: a(n) = 8n^2 + 8n + 4.
A122919: Inverse of Riordan array (1/(1+x+x^2),x/(1+x)^2).
A237832: Number of partitions of n such that (greatest part) - (least part) = number of parts.
A244385: Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + ... + n^37 is prime.
A272423: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 473", based on the 5-celled von Neumann neighborhood.
A277449: Numbers n such that there is exactly one nontrivial square n-gonal number.

Number of the day: 4274

Properties of the number 4274:

4274 = 2 × 2137 is semiprime and squarefree.
4274 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 2136 totatives.
4274 has an emirp digit sum 17 in base 10.
4274 has sum of divisors equal to 6414 which is a sphenic number.
4274 = 7² + 65² is the sum of 2 positive squares in 1 way.
4274 = 15² + 32² + 55² is the sum of 3 positive squares.
4274² = 910² + 4176² is the sum of 2 positive squares in 1 way.
4274² is the sum of 3 positive squares.
4274 is a proper divisor of 263⁸⁹ - 1.
4274 = '4' + '274' is the concatenation of 2 semiprime numbers.
4274 is an emirpimes in (at least) the following bases: 3, 4, 13, 14, 16, 17, 25, 27, 28, 29, 31, 34, 35, 36, 38, 39, 44, 45, 52, 56, 57, 61, 64, 68, 69, 70, 73, 75, 80, 87, 89, 91, 94, 97, and 99.
4274 is palindromic in (at least) the following bases: -35, and -48.

The number 4274 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007498: Unique period lengths of primes mentioned in A007615.
A051627: Periods associated with A040017.
A125754: Numbers n whose reverse binary representation has the following property: let a 0 mean "halving" and a 1 mean "k -> 3k+1". The number describes an operation k -> f_n(k). If the equation f_n(k) = k has an integer solution, n is a term in the sequence.
A125756: Numbers n whose reverse binary representation has the following property: let a 0 mean "halving" and a 1 mean "k -> 3k+1". The number describes an operation k -> f_n(k). If the equation f_n(k) = k has a positive integer solution, n is a term in the sequence.
A138940: Indices n such that A019328(n) = Phi(n,10) is prime, where Phi is a cyclotomic polynomial.
A201077: G.f.: 1 / Product_{i>=1} (1-q^(2*i-1))^2*(1-q^(12*i-8))*(1-q^(12*i-6))*(1-q^(12*i-4))*(1-q^(12*i)).
A217891: T(n,k)=Number of n element 1..n arrays with each element the minimum of k adjacent elements of a permutation of 1..n+k-1 of n+k-1 elements
A267167: Growth series for affine Coxeter group B_4.
A275188: Positions of 8 in A274640.
A278784: Numbers n such that A000041(n) is of the form 2^7 * k for odd k.

Number of the day: 3045

Properties of the number 3045:

3045 = 3 × 5 × 7 × 29 is the 2608^th composite number and is squarefree.
3045 has 4 distinct prime factors, 16 divisors, 15 antidivisors and 1344 totatives.
3045 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 3045 results in a semiprime.
3045 = 1523² - 1522² = 509² - 506² = 307² - 302² = 221² - 214² = 109² - 94² = 83² - 62² = 67² - 38² = 61² - 26² is the difference of 2 nonnegative squares in 8 ways.
3045 is the sum of 2 positive triangular numbers.
3045 is the difference of 2 positive pentagonal numbers in 3 ways.
3045 = 20² + 23² + 46² is the sum of 3 positive squares.
3045² = 2100² + 2205² = 357² + 3024² = 504² + 3003² = 1827² + 2436² is the sum of 2 positive squares in 4 ways.
3045² is the sum of 3 positive squares.
3045 is a proper divisor of 349² - 1.
3045 is palindromic in (at least) base 86.
3045 in base 12 = 1919 and consists of only the digits '1' and '9'.
3045 in base 14 = 1177 and consists of only the digits '1' and '7'.
3045 in base 19 = 885 and consists of only the digits '5' and '8'.
3045 in base 22 = 669 and consists of only the digits '6' and '9'.
3045 in base 27 = 44l and consists of only the digits '4' and 'l'.

The number 3045 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000266: E.g.f. exp(-x^2/2) / (1-x).
A005476: a(n) = n*(5*n - 1)/2.
A007059: Number of balanced ordered trees with n nodes.
A022289: a(n) = n*(31*n + 1)/2.
A024966: 7 times triangular numbers: 7n(n+1)/2.
A034828: a(n) = [n^2/4]*n/2.
A055561: Numbers n such that there are precisely 3 groups of order n.
A079500: Number of compositions of the integer n in which the first part is >= the other parts.
A094416: Array read by antidiagonals: generalized ordered Bell numbers Bo(r,n).
A128396: Numbers n such that n^2 divides 16^n-1.

Number of the day: 7172017

Happy Yellow Pig Day!

Properties of the number 7172017:

7172017 is a cyclic number.
7172017 = 1877 × 3821 is semiprime and squarefree.
7172017 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 7166320 totatives.
7172017 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 7172017 results in a sphenic number.
7172017 = 3586009² - 3586008² = 2849² - 972² is the difference of 2 nonnegative squares in 2 ways.
7172017 is the sum of 2 positive triangular numbers.
7172017 is the difference of 2 positive pentagonal numbers in 1 way.
7172017 = 1264² + 2361² = 444² + 2641² is the sum of 2 positive squares in 2 ways.
7172017 = 86² + 189² + 2670² is the sum of 3 positive squares.
7172017² = 4386508² + 5674185² = 3976625² + 5968608² = 2345208² + 6777745² = 2289940² + 6796617² is the sum of 2 positive squares in 4 ways.
7172017² is the sum of 3 positive squares.
7172017 is a proper divisor of 137⁷⁶⁴ - 1.
7172017 is an emirpimes in (at least) the following bases: 2, 8, 13, 19, 21, 22, 25, 26, 27, 31, 34, 35, 37, 38, 39, 44, 45, 51, 53, 59, 61, 67, 73, 75, 77, 80, 82, 83, 85, 87, 89, 91, 93, and 97.