A197953 a(n) = 1 + Sum_{d|n, d>1} d * a(n/d).

1, 3, 4, 11, 6, 24, 8, 43, 22, 38, 12, 128, 14, 52, 54, 171, 18, 186, 20, 206, 74, 80, 24, 640, 56, 94, 130, 284, 30, 494, 32, 683, 114, 122, 118, 1226, 38, 136, 134, 1038, 42, 682, 44, 440, 432, 164, 48, 3072, 106, 488, 174, 518, 54, 1374, 182, 1436, 194

Offset: 1

Author

Paul D. Hanna, Oct 19 2011

Keywords

• nonn

Comments

Logarithmic derivative of A129374, where g.f. G(x) of A129374 satisfies: G(x) = 1/(1-x) * G(x^2)*G(x^3)*G(x^4)*...*G(x^n)*...

Examples

			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 +...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Paul D. Hanna)

Crossrefs

Cf. A067824, A129374, A307607.

Programs

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)}

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.