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

3,6

Comments

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.

Links

Table of n, a(n) for n=3..87.

Formula

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

Mathematica

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

Crossrefs

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

Sequence in context: A240131 A029640 A029658 * A239452 A368468 A069930

Adjacent sequences: A332886 A332887 A332888 * A332890 A332891 A332892

Keyword

nonn

Author

Clark Kimberling, Mar 11 2020

Status

approved