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A197953 a(n) = 1 + Sum_{d|n, d>1} d * a(n/d). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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)*...

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

Cf. A067824, A129374, A307607.

Sequence in context: A335887 A335888 A328851 * A198299 A175317 A056045

Adjacent sequences:  A197950 A197951 A197952 * A197954 A197955 A197956

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 19 2011

STATUS

approved

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Last modified September 17 07:35 EDT 2021. Contains 347478 sequences. (Running on oeis4.)