A341141 Number of partitions of n into 4 distinct prime powers (including 1).

1, 1, 1, 2, 3, 4, 5, 7, 7, 9, 9, 11, 12, 15, 15, 19, 18, 21, 21, 26, 25, 30, 29, 35, 32, 39, 37, 45, 43, 52, 50, 58, 54, 62, 61, 71, 66, 75, 74, 81, 78, 89, 85, 96, 93, 102, 99, 110, 103, 115, 117, 122, 120, 131, 127, 136, 136, 139, 142, 153, 147, 154, 160, 163, 165, 177, 175

Offset

10,4

Links

Table of n, a(n) for n=10..76.

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, 4):
seq(a(n), n=10..76);  # 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, 4];
Table[a[n], {n, 10, 76}] (* Jean-François Alcover, Jul 13 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000961, A010055, A341122, A341132, A341133, A341140, A341142, A341143, A341144, A341145.

Sequence in context: A339378 A341156 A352921 * A325353 A117174 A320466

Adjacent sequences: A341138 A341139 A341140 * A341142 A341143 A341144

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved