A294334 Number of partitions of n into triangular numbers dividing n.

1, 1, 1, 2, 1, 1, 4, 1, 1, 4, 2, 1, 9, 1, 1, 7, 1, 1, 16, 1, 3, 9, 1, 1, 25, 1, 1, 10, 2, 1, 74, 1, 1, 12, 1, 1, 50, 1, 1, 14, 5, 1, 85, 1, 1, 35, 1, 1, 81, 1, 6, 18, 1, 1, 100, 2, 3, 20, 1, 1, 544, 1, 1, 46, 1, 1, 145, 1, 1, 24, 8, 1, 219, 1, 1, 81, 1, 1, 197, 1, 9, 28, 1, 1, 628, 1, 1, 30, 1, 1, 2264, 2, 1, 32, 1, 1

Offset: 0

Author

Ilya Gutkovskiy, Oct 28 2017

Keywords

• nonn
• look

Examples

			a(6) = 4 because 6 has 4 divisors {1, 2, 3, 6} among which 3 are triangular numbers {1, 3, 6} therefore we have [6], [3, 3], [3, 1, 1, 1] and [1, 1, 1, 1, 1, 1].
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to partitions
• Index to sequences related to polygonal numbers

Crossrefs

Cf. A000217, A007294, A007862, A018818, A112886, A284345.

Programs

Mathematica

Table[SeriesCoefficient[Product[1/(1 - Boole[Mod[n, k] == 0 && IntegerQ[Sqrt[8 k + 1]]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 95}]

Formula

a(n) = 1 if n in A112886.