A341144 Number of partitions of n into 7 distinct prime powers (including 1).

1, 1, 1, 1, 2, 3, 3, 4, 6, 8, 8, 10, 12, 15, 16, 22, 23, 29, 30, 37, 40, 50, 50, 63, 68, 79, 81, 99, 101, 121, 127, 147, 153, 182, 182, 214, 224, 253, 262, 304, 309, 351, 365, 405, 421, 477, 485, 541, 563, 614, 634, 706, 719, 791, 823, 888, 919, 1006, 1029, 1115, 1164

Offset

30,5

Links

Table of n, a(n) for n=30..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, 7):
seq(a(n), n=30..90);  # 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, 7];
Table[a[n], {n, 30, 90}] (* Jean-François Alcover, Feb 22 2022, after Alois P. Heinz *)

Crossrefs

Cf. A000961, A010055, A341125, A341132, A341136, A341140, A341141, A341142, A341143, A341145.

Sequence in context: A277579 A241447 A081230 * A365831 A036021 A036025

Adjacent sequences: A341141 A341142 A341143 * A341145 A341146 A341147

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 05 2021

Status

approved