Friday, December 23, 2016

Number of the day: 2945

Properties of the number 2945:

2945 = 5 × 19 × 31 is a sphenic number and squarefree.
2945 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 2160 totatives.
2945 has an oblong digit sum 20 in base 10.
2945 = 14732 - 14722 = 2972 - 2922 = 872 - 682 = 632 - 322 is the difference of 2 nonnegative squares in 4 ways.
2945 is the difference of 2 positive pentagonal numbers in 3 ways.
2945 = 22 + 52 + 542 is the sum of 3 positive squares.
29452 = 17672 + 23562 is the sum of 2 positive squares in 1 way.
29452 is the sum of 3 positive squares.
2945 is a divisor of 18612 - 1.
2945 is palindromic in (at least) the following bases: 46, 94, -64, and -92.
2945 in base 20 = 775 and consists of only the digits '5' and '7'.
2945 in base 45 = 1KK and consists of only the digits '1' and 'K'.
2945 in base 46 = 1I1 and consists of only the digits '1' and 'I'.

The number 2945 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A011257: Geometric mean of phi(n) and sigma(n) is an integer.
A026797: Number of partitions of n in which the least part is 4.
A038691: Prime race 4k-1 vs. 4k+1 is tied at n-th prime.
A045944: Rhombic matchstick numbers: n*(3*n+2).
A050059: a(n)=a(n-1)+a(m), where m=2n-2-2^(p+1) and 2^p<n-1<=2^(p+1), for n >= 4.
A081377: Numbers n such that the set of prime divisors of phi(n) is equal to the set of prime divisors of sigma(n).
A089558: a(n)=A089551(n)/2.
A139593: A139276(n) followed by A139272(n+1).
A219038: Numbers n such that 3^n - 14 is prime.
A246326: Total number of ON cells at stage n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 454".

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