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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.
Logarithmic derivative of A198301.
LINKS
FORMULA
L.g.f.: Sum_{n>=1} Sum_{k>=1} sigma(n,k) * x^(n*k)/n.
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 + ...
MATHEMATICA
a[n_] := DivisorSum[n, # * DivisorSigma[#, n/#] &]; Array[a, 40] (* Amiram Eldar, Aug 18 2023 *)
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 27 2012
STATUS
approved

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Last modified July 17 18:09 EDT 2024. Contains 374377 sequences. (Running on oeis4.)