Saturday, July 22, 2017

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.

Friday, July 21, 2017

Number of the day: 1844

Properties of the number 1844:

1844 = 22 × 461 is the 1561th 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.

Thursday, July 20, 2017

Number of the day: 6052

Properties of the number 6052:

6052 = 22 × 17 × 89 is the 5262th 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.

Wednesday, July 19, 2017

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.

Tuesday, July 18, 2017

Number of the day: 3045

Properties of the number 3045:

3045 = 3 × 5 × 7 × 29 is the 2608th 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.

Monday, July 17, 2017

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.

Sunday, July 16, 2017

Number of the day: 81813

Properties of the number 81813:

81813 = 3 × 27271 is semiprime and squarefree.
81813 has 2 distinct prime factors, 4 divisors, 33 antidivisors and 54540 totatives.
81813 has a semiprime digit sum 21 in base 10.
81813 has a Fibonacci digit sum 21 in base 10.
81813 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 81813 results in a sphenic number.
81813 = 409072 - 409062 = 136372 - 136342 is the difference of 2 nonnegative squares in 2 ways.
81813 is the sum of 2 positive triangular numbers.
81813 is the difference of 2 positive pentagonal numbers in 1 way.
81813 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
81813 = 12 + 42 + 2862 is the sum of 3 positive squares.
818132 is the sum of 3 positive squares.
81813 is a proper divisor of 190154 - 1.
81813 is an emirpimes in (at least) the following bases: 3, 6, 7, 9, 15, 19, 33, 35, 48, 51, 55, 61, 67, 71, 78, 81, 85, and 99.
81813 is palindromic in (at least) base -55.
81813 in base 54 = S33 and consists of only the digits '3' and 'S'.

The number 81813 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A053948: Numbers n such that n^2 contains only digits {3,6,9}.
A137041: Numbers n such that n and the square of n use only the digits 1, 3, 6, 8 and 9.