Tuesday, April 3, 2018

Number of the day: 59178

Properties of the number 59178:

59178 = 2 × 3 × 7 × 1409 is the 53194th composite number and is squarefree.
59178 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 16896 totatives.
59178 has a sphenic digit sum 30 in base 10.
59178 has an oblong digit sum 30 in base 10.
Reversing the decimal digits of 59178 results in a sphenic number.
59178 is the sum of 2 positive triangular numbers.
59178 is the difference of 2 positive pentagonal numbers in 4 ways.
59178 = 162 + 292 + 2412 is the sum of 3 positive squares.
591782 = 66782 + 588002 is the sum of 2 positive squares in 1 way.
591782 is the sum of 3 positive squares.
59178 is a proper divisor of 18614 - 1.
59178 is palindromic in (at least) base -58.
59178 in base 20 = 77ii and consists of only the digits '7' and 'i'.
59178 in base 57 = ICC and consists of only the digits 'C' and 'I'.

The number 59178 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A210167: Number of (n+1)X2 0..3 arrays containing all values 0..3 with every 2X2 subblock having two or four distinct values, and new values 0..3 introduced in row major order
A210172: Number of (n+1)X7 0..3 arrays containing all values 0..3 with every 2X2 subblock having two or four distinct values, and new values 0..3 introduced in row major order
A210174: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays containing all values 0..3 with every 2X2 subblock having two or four distinct values, and new values 0..3 introduced in row major order
A286560: Compound filter (summands of A004001 & summands of A005185): a(n) = P(A286541(n), A286559(n)), where P(n,k) is sequence A000027 used as a pairing function, with a(1) = a(2) = 0.
A294609: Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1-j*x^j)^(j^(k*j)) in powers of x.
A294950: Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} 1/(1-j^(k*j)*x^j)^j in powers of x.

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