A102291 Total number of prime parts in all compositions of n.

0, 0, 1, 3, 7, 18, 42, 98, 222, 497, 1100, 2413, 5250, 11350, 24398, 52193, 111180, 235949, 499074, 1052502, 2213710, 4644833, 9724492, 20318637, 42376578, 88231765, 183420748, 380755932, 789340736, 1634339217, 3379993922, 6982618822, 14410499598, 29711523105

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..3313

Formula

G.f.: Sum_{k>=1} x^prime(k)*(1-x)^2/(1-2*x)^2.

a(n) = Sum_{k=1..floor(n/2)} k * A224344(n,k). - Alois P. Heinz, Aug 06 2019

Maple

a:= proc(n) option remember; `if`(n=0, 0, add(a(n-j)+
      `if`(isprime(j), ceil(2^(n-j-1)), 0), j=1..n))
    end:
seq(a(n), n=0..33);  # Alois P. Heinz, Aug 06 2019

Mathematica

a[n_] := a[n] = If[n==0, 0, Sum[a[n-j] + If[PrimeQ[j], Ceiling[2^(n-j-1)], 0], {j, 1, n}]];
a /@ Range[0, 33] (* Jean-François Alcover, Oct 30 2020, after Alois P. Heinz *)

Crossrefs

Cf. A037032, A224344, A336632.

Sequence in context: A356938 A208771 A036884 * A034691 A317546 A319001

Adjacent sequences: A102288 A102289 A102290 * A102292 A102293 A102294

Keyword

easy,nonn

Author

Vladeta Jovovic, Feb 19 2005

Extensions

More terms from Joshua Zucker, May 10 2006

Status

approved