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 A343465 a(n) = -(1/n) * Sum_{d|n} phi(n/d) * (-3)^d. 2
 3, -3, 11, -21, 51, -119, 315, -831, 2195, -5883, 16107, -44357, 122643, -341487, 956635, -2690841, 7596483, -21522347, 61171659, -174342165, 498112275, -1426403751, 4093181691, -11767920107, 33891544419, -97764009003, 282429537947, -817028472645, 2366564736723, -6863037262207 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..30. FORMULA G.f.: Sum_{k>=1} phi(k) * log(1 + 3*x^k) / k. a(n) = -(1/n) * Sum_{k=1..n} (-3)^gcd(n,k). Product_{n>=1} 1 / (1 - x^n)^a(n) = g.f. for A032308. Product_{n>=1} (1 - x^n)^a(n) = g.f. for A261582. MATHEMATICA Table[-(1/n) Sum[EulerPhi[n/d] (-3)^d, {d, Divisors[n]}], {n, 1, 30}] nmax = 30; CoefficientList[Series[Sum[EulerPhi[k] Log[1 + 3 x^k]/k, {k, 1, nmax}], {x, 0, nmax}], x] // Rest CROSSREFS Cf. A000010, A001867, A032308, A038064, A074763, A261582, A343466, A343467. Sequence in context: A163932 A007022 A011950 * A289883 A280564 A281284 Adjacent sequences: A343462 A343463 A343464 * A343466 A343467 A343468 KEYWORD sign AUTHOR Ilya Gutkovskiy, Apr 16 2021 STATUS approved

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Last modified August 13 04:16 EDT 2024. Contains 375113 sequences. (Running on oeis4.)