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 A343467 a(n) = -(1/n) * Sum_{d|n} phi(n/d) * (-5)^d. 2
 5, -10, 45, -160, 629, -2590, 11165, -48910, 217045, -976258, 4438925, -20346440, 93900245, -435959830, 2034505661, -9536767660, 44878791365, -211927519090, 1003867701485, -4768372070128, 22706531350485, -108372079190350, 518301258916445, -2483526875847690, 11920928955078629 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..25. FORMULA G.f.: Sum_{k>=1} phi(k) * log(1 + 5*x^k) / k. a(n) = -(1/n) * Sum_{k=1..n} (-5)^gcd(n,k). Product_{n>=1} 1 / (1 - x^n)^a(n) = g.f. for A261569. MATHEMATICA Table[-(1/n) Sum[EulerPhi[n/d] (-5)^d, {d, Divisors[n]}], {n, 1, 25}] nmax = 25; CoefficientList[Series[Sum[EulerPhi[k] Log[1 + 5 x^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest CROSSREFS Cf. A000010, A001869, A038066, A074763, A261569, A343465, A343466. Sequence in context: A328605 A122173 A083515 * A103971 A270085 A035406 Adjacent sequences: A343464 A343465 A343466 * A343468 A343469 A343470 KEYWORD sign AUTHOR Ilya Gutkovskiy, Apr 16 2021 STATUS approved

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Last modified May 26 16:43 EDT 2024. Contains 372840 sequences. (Running on oeis4.)