A339243 Number of partitions of n into divisors of n where every part appears at least 2 times.

0, 1, 1, 2, 1, 4, 1, 5, 3, 6, 1, 15, 1, 8, 7, 16, 1, 29, 1, 32, 9, 12, 1, 104, 5, 14, 13, 60, 1, 171, 1, 81, 15, 18, 14, 448, 1, 20, 17, 326, 1, 426, 1, 147, 99, 24, 1, 1675, 7, 173, 23, 205, 1, 902, 23, 809, 25, 30, 1, 8616, 1, 32, 183, 682, 27, 1629, 1, 354, 31, 1309

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..10401

Index entries for sequences related to partitions

Formula

a(n) = [x^n] Product_{d|n} (1 + x^(2*d) / (1 - x^d)).

Example

a(15) = 7 because we have [5, 5, 5], [3, 3, 3, 3, 3], [5, 5, 1, 1, 1, 1, 1], [3, 3, 3, 3, 1, 1, 1], [3, 3, 3, 1, 1, 1, 1, 1, 1], [3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

Mathematica

Table[SeriesCoefficient[Product[1 + x^(2 d)/(1 - x^d), {d, Divisors[n]}], {x, 0, n}], {n, 1, 70}]

Prog

(PARI) A339243(n) = { my(p=1); fordiv(n, d, p *= (1 + 'x^(2*d) / (1 - 'x^d))); polcoeff(Ser(p, 'x, 1+n), n); }; \\ Antti Karttunen, Jan 22 2025

Crossrefs

Cf. A000040 (positions of 1's), A007690, A018818, A027750.

Sequence in context: A322100 A277100 A337363 * A214579 A083711 A339619

Adjacent sequences: A339240 A339241 A339242 * A339244 A339245 A339246

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 28 2020

Status

approved