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A197953 a(n) = 1 + Sum_{d|n, d>1} d * a(n/d). 3

%I

%S 1,3,4,11,6,24,8,43,22,38,12,128,14,52,54,171,18,186,20,206,74,80,24,

%T 640,56,94,130,284,30,494,32,683,114,122,118,1226,38,136,134,1038,42,

%U 682,44,440,432,164,48,3072,106,488,174,518,54,1374,182,1436,194

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

%C 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)*...

%H Seiichi Manyama, <a href="/A197953/b197953.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Paul D. Hanna)

%F 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.

%e 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 +...

%e where

%e L(x) = -log(1-x) + L(x^2) + L(x^3) + L(x^4) + L(x^5) +...+ L(x^n) +...

%e also, exp(L(x)) is the g.f. of A129374:

%e exp(L(x)) = 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 8*x^5 + 15*x^6 + 20*x^7 +...

%o (PARI) {a(n)=sumdiv(n,d,d*if(d==1,1,a(n/d)))}

%o (PARI) /* L.g.f. satisfies: L(x) = -log(1-x) + Sum_{n>1} L(x^n) */

%o {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)}

%Y Cf. A067824, A129374, A307607.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Oct 19 2011

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Last modified October 20 10:43 EDT 2021. Contains 348100 sequences. (Running on oeis4.)