The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A102291 Total number of prime parts in all compositions of n. 10
 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 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 18 14:29 EDT 2024. Contains 374388 sequences. (Running on oeis4.)