A341145 Number of partitions of n into 8 distinct prime powers (including 1).

1, 0, 1, 1, 2, 1, 2, 3, 5, 5, 6, 7, 10, 10, 13, 16, 19, 21, 26, 30, 34, 37, 44, 52, 58, 66, 73, 85, 94, 106, 115, 136, 146, 165, 178, 204, 215, 248, 263, 298, 318, 356, 372, 426, 443, 494, 520, 585, 603, 681, 702, 781, 815, 906, 929, 1044, 1071, 1178, 1223

Offset

39,5

Links

Table of n, a(n) for n=39..97.

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, 8):
seq(a(n), n=39..97);  # Alois P. Heinz, Feb 05 2021

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, 8];
Table[a[n], {n, 39, 97}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)

Crossrefs

Cf. A000961, A010055, A341126, A341132, A341137, A341140, A341141, A341142, A341143, A341144.

Sequence in context: A125596 A351962 A253026 * A204994 A277253 A309494

Adjacent sequences: A341142 A341143 A341144 * A341146 A341147 A341148

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved