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A198302 a(n) = Sum_{d|n} d * sigma(n/d, d). 1

%I

%S 1,5,7,21,11,65,15,133,106,245,23,1077,27,1041,1637,3365,35,9992,39,

%T 18361,16401,22841,47,134461,15686,106917,179494,355173,59,1220075,63,

%U 1593189,1952705,2228909,631005,13778268,75,9962313,20732901,34805473,83,113693883

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

%C Here sigma(n,k) is the sum of the k-th powers of the divisors of n.

%F L.g.f.: Sum_{n>=1} Sum_{k>=1} sigma(n,k) * x^(n*k)/n.

%F Logarithmic derivative of A198301.

%e L.g.f.: L(x) = x + 5*x^2/2 + 7*x^3/3 + 21*x^4/4 + 11*x^5/5 + 65*x^6/6 +...

%e Exponentiation yields the g.f. of A198301:

%e exp(L(x)) = 1 + x + 3*x^2 + 5*x^3 + 12*x^4 + 18*x^5 + 42*x^6 + 62*x^7 + 131*x^8 + 206*x^9 + 398*x^10 +...+ A198301(n)*x^n +...

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

%o (PARI) {a(n)=n*polcoeff(sum(m=1,n,sum(k=1,n\m,sigma(m,k)*x^(m*k)/m)+x*O(x^n)),n)}

%Y Cf. A198301 (exp), A185301, A198299.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jan 27 2012

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Last modified October 28 06:29 EDT 2021. Contains 348313 sequences. (Running on oeis4.)