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A294334 Number of partitions of n into triangular numbers dividing n. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..95.

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

AUTHOR

Ilya Gutkovskiy, Oct 28 2017

STATUS

approved

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Last modified November 15 04:00 EST 2018. Contains 317225 sequences. (Running on oeis4.)