OFFSET
1,4
COMMENTS
a(n)/a(n-1) -> 1.476229...=1/x, where x satisfies the Sum x^p(n)=1 equation, i.e. x^2+x^3+x^5+x^7+x^11+... =1. (What constant is it?)
LINKS
T. D. Noe, Table of n, a(n) for n=1..500
EXAMPLE
a(12) = 36 = a(12-2)+a(12-3)+a(12-5)+a(12-7)+a(12-11) = a(10)+a(9)+a(7)+a(5)+a(1) = 16+12+5+2+1 = 36.
MATHEMATICA
a[1] = a[2] = 1; a[n_] := a[n] = Sum[a[n - Prime[k]], {k, 1, PrimePi[n]}]; Table[a[n], {n, 1, 38}] (* Jean-François Alcover, Mar 22 2011 *)
PROG
(Haskell)
import Data.List (genericIndex)
a078465 n = a078465_list `genericIndex` (n-1)
a078465_list = 1 : 1 : f 3 where
f x = (sum $ map (a078465 . (x -)) $
takeWhile (< x) a000040_list) : f (x + 1)
-- Reinhard Zumkeller, Jul 20 2012
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
Miklos Kristof, Jan 02 2003
STATUS
approved