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A220427 G.f.: exp( Sum_{n>=1} A005064(n)*x^n/n ), where A005064(n) = sum of cubes of primes dividing n.

%I A220427 #7 Jan 10 2025 18:25:02
%S A220427 1,0,4,9,10,61,65,239,440,791,2172,3211,8018,14292,27174,56064,96092,
%T A220427 195616,345831,643733,1189397,2102921,3864549,6804894,12150956,
%U A220427 21419322,37460309,65511385,113436266,195931822,336547491,575446427,979007055,1660337942,2800856388
%N A220427 G.f.: exp( Sum_{n>=1} A005064(n)*x^n/n ), where A005064(n) = sum of cubes of primes dividing n.
%e A220427 G.f.: A(x) = 1 + 4*x^2 + 9*x^3 + 10*x^4 + 61*x^5 + 65*x^6 + 239*x^7 +...
%e A220427 where
%e A220427 log(A(x)) = 8*x^2/2 + 27*x^3/3 + 8*x^4/4 + 125*x^5/5 + 35*x^6/6 + 343*x^7/7 + 8*x^8/8 + 27*x^9/9 + 133*x^10/10 + 1331*x^11/11 + 35*x^12/12 + 2197*x^13/13 + 351*x^14/14 + 152*x^15/15 +...+ A005064(n)*x^n/n +...
%o A220427 (PARI) {a(n)=polcoeff(exp(sum(k=1,n+1,sumdiv(k,d,isprime(d)*d^3)*x^k/k)+x*O(x^n)),n)}
%o A220427 for(n=0,40,print1(a(n),", "))
%Y A220427 Cf. A005064, A219224.
%K A220427 nonn
%O A220427 0,3
%A A220427 _Paul D. Hanna_, Dec 14 2012