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 A346760 a(n) = Sum_{d|n} mu(n/d) * binomial(d,3). 1
 0, 0, 1, 4, 10, 19, 35, 52, 83, 110, 165, 196, 286, 329, 444, 504, 680, 713, 969, 1016, 1294, 1375, 1771, 1752, 2290, 2314, 2841, 2908, 3654, 3476, 4495, 4400, 5290, 5304, 6500, 6124, 7770, 7467, 8852, 8688, 10660, 9802, 12341, 11700, 13652, 13409, 16215, 14768, 18389, 17190 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS FORMULA G.f.: Sum_{k>=1} mu(k) * x^(3*k) / (1 - x^k)^4. a(n) = (A059376(n) - 3 * A007434(n) + 2 * A000010(n)) / 6. MATHEMATICA Table[Sum[MoebiusMu[n/d] Binomial[d, 3], {d, Divisors[n]}], {n, 1, 50}] nmax = 50; CoefficientList[Series[Sum[MoebiusMu[k] x^(3 k)/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x] // Rest PROG (PARI) a(n) = sumdiv(n, d, moebius(n/d)*binomial(d, 3)); \\ Michel Marcus, Aug 03 2021 CROSSREFS 3rd column of A020921. Cf. A000010, A000292, A007434, A059376, A102309, A117108, A346761. Sequence in context: A301215 A155389 A155316 * A038418 A301206 A057318 Adjacent sequences:  A346757 A346758 A346759 * A346761 A346762 A346763 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Aug 02 2021 STATUS approved

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Last modified June 30 02:41 EDT 2022. Contains 354913 sequences. (Running on oeis4.)