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

0,4

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

Formula

a(n) = 1 if n in A112886.

Example

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].

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}]

Crossrefs

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

Sequence in context: A141450 A209690 A061462 * A122578 A208648 A005131

Adjacent sequences: A294331 A294332 A294333 * A294335 A294336 A294337

Keyword

nonn,look

Author

Ilya Gutkovskiy, Oct 28 2017

Status

approved