A332888 -id:A332888 - cp's OEIS frontend

A332889 a(n) = number of strict partition numbers >1 that are proper divisors of the n-th strict partition number.

0, 0, 0, 1, 0, 2, 2, 2, 4, 2, 3, 1, 1, 3, 1, 1, 5, 4, 3, 0, 3, 1, 1, 3, 8, 3, 5, 3, 4, 6, 5, 6, 3, 2, 7, 10, 1, 1, 9, 2, 4, 3, 7, 11, 3, 6, 9, 1, 0, 1, 9, 3, 3, 2, 1, 6, 11, 8, 2, 1, 7, 2, 6, 2, 4, 12, 3, 0, 4, 8, 4, 4, 1, 7, 0, 1, 9, 7, 5, 5, 1, 1, 6, 5, 4

Offset: 3

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Clark Kimberling, Mar 11 2020

nonn

Let p(n) = number of strict partitions of n. Then p(11) = 12, which is divisible by these 6 strict partition numbers: p(2) = 1, p(3) = 2, p(5) = 3, p(6) = 4, p(8) = 6, and p(11) = 12; discounting 1 and 12 leaves a(11) = 4 divisors.

Cf. A000009 (strict partition numbers), A322887, A332888.

p[n_] := PartitionsQ[n]; t[n_] := Table[p[k], {k, 0, n}]
-2+Table[Length[Intersection[t[n], Divisors[p[n]]]], {n, 3, 130}]

a(n) = A332888(n) - 2 for n >= 3.

cp's OEIS Frontend

A332889 a(n) = number of strict partition numbers >1 that are proper divisors of the n-th strict partition number.

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