A341142 Number of partitions of n into 5 distinct prime powers (including 1).

1, 0, 1, 2, 3, 3, 5, 5, 7, 8, 10, 12, 15, 15, 18, 21, 23, 26, 31, 33, 36, 41, 43, 48, 52, 58, 62, 72, 72, 82, 85, 95, 97, 112, 112, 125, 127, 142, 142, 161, 159, 181, 180, 200, 196, 222, 217, 243, 239, 269, 261, 291, 284, 316, 308, 341, 332, 370, 358, 394, 381, 427, 414, 456

Offset

15,4

Links

Alois P. Heinz, Table of n, a(n) for n = 15..5000

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, 5):
seq(a(n), n=15..78);  # Alois P. Heinz, Feb 05 2021

Mathematica

q[n_] := q[n] = PrimeNu[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, 5];
Table[a[n], {n, 15, 78}] (* Jean-François Alcover, Jul 13 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000961, A010055, A341123, A341132, A341134, A341140, A341141, A341143, A341144, A341145.

Sequence in context: A280271 A145834 A339246 * A130006 A099609 A350865

Adjacent sequences: A341139 A341140 A341141 * A341143 A341144 A341145

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved