|
|
A341112
|
|
Number of partitions of n into 3 prime powers (including 1).
|
|
9
|
|
|
1, 1, 2, 3, 4, 4, 6, 6, 8, 8, 10, 9, 12, 10, 13, 12, 15, 13, 17, 15, 18, 15, 19, 16, 21, 17, 23, 18, 24, 19, 27, 23, 30, 24, 32, 25, 32, 26, 34, 26, 36, 26, 36, 28, 38, 28, 40, 30, 42, 32, 43, 30, 45, 32, 47, 35, 49, 30, 50, 35, 51, 36, 53, 35, 55, 37, 54, 40, 57, 36, 61, 40, 61
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
3,3
|
|
LINKS
|
|
|
MAPLE
|
q:= proc(n) option remember; nops(ifactors(n)[2])<2 end:
b:= proc(n, i, t) option remember; `if`(n=0,
`if`(t=0, 1, 0), `if`(i<1 or t<1, 0, b(n, i-1, t)+
`if`(q(i), b(n-i, min(n-i, i), t-1), 0)))
end:
a:= n-> b(n$2, 3):
|
|
MATHEMATICA
|
q[n_] := q[n] = Length[FactorInteger[n]] < 2;
b[n_, i_, t_] := b[n, i, t] = If[n == 0,
If[t == 0, 1, 0], If[i < 1 || t < 1, 0, b[n, i - 1, t] +
If[q[i], b[n - i, Min[n - i, i], t - 1], 0]]];
a[n_] := b[n, n, 3];
|
|
CROSSREFS
|
Cf. A000961, A010055, A071330, A282064, A307727, A307825, A341122, A341123, A341124, A341125, A341126, A341127.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|