OFFSET
1,2
COMMENTS
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Paul D. Hanna)
FORMULA
L.g.f. satisfies: L(x) = -log(1-x) + Sum_{n>1} L(x^n), where L(x) = Sum_{n>=1} a(n)*x^n/n.
EXAMPLE
L.g.f.: L(x) = x + 3*x^2/2 + 4*x^3/3 + 11*x^4/4 + 6*x^5/5 + 24*x^6/6 +...
where
L(x) = -log(1-x) + L(x^2) + L(x^3) + L(x^4) + L(x^5) +...+ L(x^n) +...
also, exp(L(x)) is the g.f. of A129374:
exp(L(x)) = 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 8*x^5 + 15*x^6 + 20*x^7 +...
PROG
(PARI) {a(n)=sumdiv(n, d, d*if(d==1, 1, a(n/d)))}
(PARI) /* L.g.f. satisfies: L(x) = -log(1-x) + Sum_{n>1} L(x^n) */
{a(n)=local(L=x, X=x+x*O(x^n)); for(i=1, n, L=-log(1-X)+sum(m=2, n, subst(L, x, x^m+x*O(x^n)))); n*polcoeff(L, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 19 2011
STATUS
approved