A332888 a(n) = number of strict partition numbers that divide the n-th strict partition number.
1, 1, 1, 2, 2, 2, 3, 2, 4, 4, 4, 6, 4, 5, 3, 3, 5, 3, 3, 7, 6, 5, 2, 5, 3, 3, 5, 10, 5, 7, 5, 6, 8, 7, 8, 5, 4, 9, 12, 3, 3, 11, 4, 6, 5, 9, 13, 5, 8, 11, 3, 2, 3, 11, 5, 5, 4, 3, 8, 13, 10, 4, 3, 9, 4, 8, 4, 6, 14, 5, 2, 6, 10, 6, 6, 3, 9, 2, 3, 11, 9, 7, 7
Offset: 0
Keywords
Examples
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; thus a(11) = 6.
Programs
-
Mathematica
p[n_] := PartitionsQ[n]; t[n_] := Table[p[k], {k, 0, n}] Table[Length[Intersection[t[n], Divisors[p[n]]]], {n, 0, 130}]
Formula
a(n) = A332889(n) + 2.