A336579 Sum of prime parts, counted without multiplicity, in all compositions of n.

0, 0, 2, 7, 14, 38, 83, 193, 421, 917, 1969, 4210, 8908, 18763, 39287, 81940, 170270, 352726, 728663, 1501711, 3088326, 6339424, 12991312, 26583389, 54323352, 110876435, 226057023, 460432903, 936963134, 1905110662, 3870698364, 7858803605, 15945759386

Offset

0,3

Links

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

Example

a(4) = 2 + 2 + 2 + 2 + 3 + 3 = 14: 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((p-> [0, `if`(j>0 and isprime(i),
       p[1]*i, 0)]+p)(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, 0}, Sum[Function[q, {0, If[j > 0 && PrimeQ[i],
     q[[1]]*i, 0]} + q][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, Mar 17 2022, after _Alois P Heinz_ *)

Crossrefs

Cf. A000040, A097939, A102712, A309561, A336516, A336632.

Sequence in context: A178748 A194590 A107373 * A176662 A018526 A329115

Adjacent sequences: A336576 A336577 A336578 * A336580 A336581 A336582

Keyword

nonn

Author

Alois P. Heinz, Jul 26 2020

Status

approved