A289627 - OEIS

A289627

a(n) = Sum_{d|n} mu(phi(d))*n/d.

1, 3, 2, 5, 5, 6, 8, 10, 7, 15, 12, 9, 13, 24, 10, 20, 17, 21, 19, 25, 17, 36, 24, 18, 25, 39, 21, 41, 29, 30, 30, 40, 25, 51, 40, 33, 37, 57, 26, 50, 41, 51, 42, 61, 35, 72, 48, 36, 55, 75, 34, 65, 53, 63, 60, 82, 38, 87, 60, 45, 61, 90, 58, 80, 65, 75, 66, 85, 49, 120, 70, 66, 73, 111, 50, 95, 95, 78, 78, 100, 63, 123, 84, 81

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OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Sum_{d|n} mu(phi(d))*n/d = Sum_{d|n} A008683(A000010(d))*n/d.

a(A000010(n)) = A163167(n).

MATHEMATICA

a[n_] := DivisorSum[n, MoebiusMu[EulerPhi[#]] * n/# &]; Array[a, 100] (* Amiram Eldar, Aug 29 2023 *)

PROG

(PARI) A289627(n) = sumdiv(n, d, moebius(eulerphi(d))*n/d);