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A198302 a(n) = Sum_{d|n} d * sigma(n/d, d). 1
1, 5, 7, 21, 11, 65, 15, 133, 106, 245, 23, 1077, 27, 1041, 1637, 3365, 35, 9992, 39, 18361, 16401, 22841, 47, 134461, 15686, 106917, 179494, 355173, 59, 1220075, 63, 1593189, 1952705, 2228909, 631005, 13778268, 75, 9962313, 20732901, 34805473, 83, 113693883 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..42.

FORMULA

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

Logarithmic derivative of A198301.

EXAMPLE

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 +...

Exponentiation yields the g.f. of A198301:

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 +...

PROG

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

(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)}

CROSSREFS

Cf. A198301 (exp), A185301, A198299.

Sequence in context: A258282 A192422 A120035 * A091154 A057424 A027152

Adjacent sequences:  A198299 A198300 A198301 * A198303 A198304 A198305

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 27 2012

STATUS

approved

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Last modified July 17 21:30 EDT 2019. Contains 325109 sequences. (Running on oeis4.)