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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

N. J. A. Sloane.

STATUS

approved

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Last modified February 24 22:51 EST 2021. Contains 341592 sequences. (Running on oeis4.)