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A007444
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Moebius transform of primes.
(Formerly M0156)
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11
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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
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OFFSET
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1,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Michel Marcus, Table of n, a(n) for n = 1..10000
N. J. A. Sloane, Transforms
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FORMULA
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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
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MATHEMATICA
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a[n_] := DivisorSum[n, Prime[#] * MoebiusMu[n/#] &]; Array[a, 200] (* Enrique Pérez Herrero, Sep 23 2020 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, prime(d)*moebius(n/d)); \\ Michel Marcus, Nov 04 2018
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CROSSREFS
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Cf. A000040, A008683.
Sequence in context: A304590 A134876 A019612 * A332309 A166476 A052950
Adjacent sequences: A007441 A007442 A007443 * A007445 A007446 A007447
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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