OFFSET
1,8
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..5000
N. J. A. Sloane, Transforms
FORMULA
Product_{k>=1} 1/(1-x^k)^{a(k)} = 1 + x + Sum_{n>=1} prime(n) * x^(n + 1).
EXAMPLE
(1-x)^(-1) * (1-x^2)^(-1) * (1-x^3)^(-1) * (1-x^4)^(-1) * (1-x^5)^(-1) * (1-x^6)^(-1) * (1-x^7) * (1-x^8)^2 * ... = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 7*x^5 + 11*x^6 + 13*x^7 + 17*x^8 + ... .
MATHEMATICA
pp = Prepend[Prime[Range[n = 100]], 1]; s = {};
For[i = 1, i <= n + 1, i++, AppendTo[s, i*pp[[i]] - Sum[s[[d]]*pp[[i - d]], {d, i - 1}]]];
Table[Sum[If[Divisible[i, d], MoebiusMu[i/d], 0]*s[[d]], {d, 1, i}]/i, {i,
n + 1}] (* Jean-François Alcover, May 10 2019 *)
CROSSREFS
KEYWORD
sign
AUTHOR
STATUS
approved