A394086 - OEIS

A394086

Number of partitions of n where the smallest part divides all others, has multiplicity at most 2, and all larger parts are distinct.

1, 2, 2, 4, 3, 6, 5, 9, 8, 12, 11, 20, 16, 24, 26, 36, 33, 50, 47, 68, 70, 88, 90, 129, 125, 159, 173, 218, 223, 294, 297, 376, 402, 482, 519, 649, 669, 808, 881, 1055, 1114, 1352, 1427, 1700, 1848, 2139, 2305, 2746, 2915, 3398, 3692, 4258, 4583, 5335, 5731

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..55.

FORMULA

G.f.: Sum_{k>=1} q^k * B(q^k), where B(q) is the g.f. of A000009.

a(n) = Sum_{d|n} A000009(d-1).

EXAMPLE

a(8) = 9 counts these partitions: 8, 71, 62, 611, 521, 44, 431, 422, 4211.

PROG

(PARI) my(N=60, q='q+O('q^N)); Vec(sum(k=1, N, q^k*prod(j=1, N\k, 1+q^(k*j))))