|
|
A341147
|
|
Number of partitions of n into 10 distinct prime powers (including 1).
|
|
1
|
|
|
1, 0, 0, 1, 1, 1, 2, 1, 3, 3, 3, 4, 7, 5, 9, 10, 12, 10, 17, 17, 23, 24, 29, 32, 44, 40, 53, 57, 71, 71, 91, 90, 113, 117, 141, 148, 181, 181, 217, 231, 268, 276, 327, 340, 397, 412, 472, 493, 571, 590, 671, 710, 794, 831, 934, 981, 1094, 1150, 1271, 1345, 1484, 1556, 1706
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
63,7
|
|
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-1), t-1), 0)))
end:
a:= n-> b(n$2, 10):
|
|
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 - 1], t - 1], 0]]];
a[n_] := b[n, n, 10];
|
|
CROSSREFS
|
Cf. A000961, A010055, A341131, A341132, A341139, A341140, A341141, A341142, A341143, A341144, A341145, A341146.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|