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 A007444 Moebius transform of primes. (Formerly M0156) 11
 2, 1, 3, 4, 9, 7, 15, 12, 18, 17, 29, 20, 39, 25, 33, 34, 57, 30, 65, 38, 53, 47, 81, 40, 86, 59, 80, 60, 107, 41, 125, 78, 103, 79, 123, 66, 155, 95, 123, 90, 177, 75, 189, 110, 132, 115, 209, 100, 210, 114, 171, 134, 239 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Michel Marcus, Table of n, a(n) for n = 1..10000 N. J. A. Sloane, Transforms FORMULA G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n) = Sum_{n>=1} prime(n)*x^n. - Ilya Gutkovskiy, Apr 25 2017 a(n) = Sum_{d|n} prime(d)*mu(n/d), where mu is the Moebius function (A008683). - Wesley Ivan Hurt, Sep 23 2020 MATHEMATICA a[n_] := DivisorSum[n, Prime[#] * MoebiusMu[n/#] &]; Array[a, 200] (* Enrique Pérez Herrero, Sep 23 2020 *) PROG (PARI) a(n) = sumdiv(n, d, prime(d)*moebius(n/d)); \\ Michel Marcus, Nov 04 2018 CROSSREFS Cf. A000040, A008683. Sequence in context: A304590 A134876 A019612 * A332309 A166476 A052950 Adjacent sequences:  A007441 A007442 A007443 * A007445 A007446 A007447 KEYWORD nonn AUTHOR STATUS approved

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Last modified November 24 07:52 EST 2020. Contains 338607 sequences. (Running on oeis4.)