A336632 Number of prime parts, counted without multiplicity, in all compositions of n.

0, 0, 1, 3, 6, 15, 33, 74, 160, 344, 731, 1544, 3237, 6753, 14022, 29009, 59819, 123010, 252341, 516560, 1055476, 2153115, 4385889, 8922556, 18131000, 36805009, 74643126, 151255021, 306267833, 619719217, 1253191291, 2532750315, 5116124712, 10329574480

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Example

a(4) = 0 + 1 + 1 + 1 + 1 + 1 + 1 + 0 = 6: 1111, 11(2), 1(2)1, (2)11, (2)2, 1(3), (3)1, 4.

Maple

b:= proc(n, i, p) option remember; `if`(n=0, [p!, 0],
      `if`(i<1, 0, add((h-> [0, `if`(j>0 and isprime(i),
       h[1], 0)]+h)(b(n-i*j, i-1, p+j)/j!), j=0..n/i)))
    end:
a:= n-> b(n$2, 0)[2]:
seq(a(n), n=0..38);

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[n == 0, {p!, 0},
     If[i < 1, 0, Sum[Function[h, {0, If[j > 0 && PrimeQ[i],
     h[[1]], 0]} + h][b[n - i*j, i - 1, p + j]/j!], {j, 0, n/i}]]];
a[n_] := b[n, n, 0][[2]];
Table[a[n], {n, 0, 38}] (* Jean-François Alcover, May 30 2022, after Alois P. Heinz *)

Crossrefs

Cf. A000040, A102291, A336579.

Sequence in context: A375617 A232973 A289006 * A152167 A105476 A000599

Adjacent sequences: A336629 A336630 A336631 * A336633 A336634 A336635

Keyword

nonn

Author

Alois P. Heinz, Jul 28 2020

Status

approved