A341132 Number of partitions of n into 2 distinct prime powers (including 1).

1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 3, 3, 3, 3, 3, 4, 3, 5, 4, 3, 2, 5, 3, 4, 4, 5, 3, 6, 3, 6, 5, 6, 4, 7, 2, 5, 4, 6, 3, 6, 3, 6, 5, 5, 2, 8, 3, 7, 4, 6, 2, 8, 3, 7, 4, 5, 2, 8, 3, 6, 4, 6, 3, 9, 2, 8, 5, 7, 2, 10, 3, 7, 6, 7, 3, 9, 2, 9, 4, 6, 4, 11, 3, 8, 4, 7, 3, 12

Offset

3,3

Links

Table of n, a(n) for n=3..90.

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, 2):
seq(a(n), n=3..90);  # 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, 2];
Table[a[n], {n, 3, 90}] (* Jean-François Alcover, Jul 13 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000961, A010055, A071330, A282062, A306433, A307726, A341140, A341141, A341142, A341143, A341144, A341145.

Sequence in context: A090617 A053693 A330324 * A291309 A280472 A068063

Adjacent sequences: A341129 A341130 A341131 * A341133 A341134 A341135

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved