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A352063
Number of ordered factorizations of 2*n + 1 into odd factors > 1.
0
1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 3, 1, 2, 4, 1, 1, 3, 3, 1, 3, 1, 1, 8, 1, 2, 3, 1, 3, 3, 1, 1, 8, 3, 1, 3, 1, 1, 8, 3, 1, 8, 1, 3, 3, 1, 3, 3, 3, 1, 8, 1, 1, 13, 1, 1, 3, 1, 3, 8, 3, 2, 3, 4, 1, 3, 1, 3, 20, 1, 1, 3, 3, 3, 8, 1, 1, 8, 3, 1, 3, 3, 1, 13, 1, 2, 8, 1, 8, 3, 1, 1
OFFSET
0,5
COMMENTS
Also number of perfect partitions of 2*n.
LINKS
Eric Weisstein's World of Mathematics, Perfect Partition
Eric Weisstein's World of Mathematics, Ordered Factorization
FORMULA
a(n) = A002033(2*n) = A074206(2*n+1).
MATHEMATICA
A074206[1] = 1; A074206[n_] := A074206[n] = Sum[If[d < n, A074206[d], 0], {d, Divisors[n]}]; a[n_] := A074206[2 n + 1]; Table[a[n], {n, 0, 90}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 04 2022
STATUS
approved