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 A163921 G.f.: A(x) = exp( Sum_{n>=1} A( sigma(n)*x )^n*x^n/n ). 0

%I #2 Mar 30 2012 18:37:18

%S 1,1,2,7,41,385,5769,139541,5551356,369312953,41588540350,

%T 7987225089655,2629160183190431,1487755631073862696,

%U 1450453417949809255147,2439516473122553169216351,7086426394313598512496200542

%N G.f.: A(x) = exp( Sum_{n>=1} A( sigma(n)*x )^n*x^n/n ).

%C Conjecture: if F(x) = exp( Sum_{n>=1} L(n)*x^n/n ) is an integer series,

%C then the g.f. that satisfies:

%C G(x) = exp( Sum_{n>=1} G( L(n)*x )^n*x^n/n ) is also an integer series.

%C Another example of this is A157675 in which L(n) = 2^n.

%e G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 41*x^4 + 385*x^5 + 5769*x^6 +...

%e log(A(x)) = A(x)*x + A(3x)^2*x^2/2 + A(4x)^3*x^3/3 + A(7x)^4*x^4/4 +...

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(sum(k=1,n,subst(A,x,sigma(k)*x+x*O(x^n))^k*x^k/k)));polcoeff(A,n)}

%Y Cf. A157675 (variant), A000203 (sigma).

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 01 2009

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Last modified October 4 16:17 EDT 2023. Contains 365887 sequences. (Running on oeis4.)