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 A359949 Multiplicative sequence with a(p) = 3*p-1 and a(p^e) = (3*e*(p-1) + 3) * p^(e-1) for e > 1 and prime p. 0
 1, 5, 8, 18, 14, 40, 20, 48, 45, 70, 32, 144, 38, 100, 112, 120, 50, 225, 56, 252, 160, 160, 68, 384, 135, 190, 189, 360, 86, 560, 92, 288, 256, 250, 280, 810, 110, 280, 304, 672, 122, 800, 128, 576, 630, 340, 140, 960, 273, 675, 400, 684, 158, 945, 448, 960, 448, 430, 176, 2016 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..60. FORMULA Dirichlet g.f.: zeta(s-1)^3 / (zeta(s) * zeta(3*s-3)). Dirichlet convolution of A000010(n) and n * A073184(n). a(n) = Sum_{k=1..n} gcd(k, n) * A073184(gcd(k, n)). MATHEMATICA f[p_, e_] := If[e == 1, 3*p - 1, (3*e*(p - 1) + 3)*p^(e - 1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 19 2023 *) PROG (PARI) a(n) = my(f=factor(n), p, e); for (k=1, #f~, p=f[k, 1]; e=f[k, 2]; f[k, 1] = if (e == 1, 3*p-1, (3*e*(p-1) + 3) * p^(e-1)); f[k, 2] = 1); factorback(f); \\ Michel Marcus, Jan 21 2023 CROSSREFS Cf. A000010, A073184. Sequence in context: A280251 A104321 A196934 * A291752 A237276 A155086 Adjacent sequences: A359946 A359947 A359948 * A359950 A359951 A359952 KEYWORD nonn,easy,mult AUTHOR Werner Schulte, Jan 19 2023 STATUS approved

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Last modified April 15 20:47 EDT 2024. Contains 371696 sequences. (Running on oeis4.)