A071570 - OEIS

A071570

a(n) = 2 * Sum_{d|n} 2^mu(d).

4, 5, 5, 7, 5, 10, 5, 9, 7, 10, 5, 14, 5, 10, 10, 11, 5, 14, 5, 14, 10, 10, 5, 18, 7, 10, 9, 14, 5, 20, 5, 13, 10, 10, 10, 20, 5, 10, 10, 18, 5, 20, 5, 14, 14, 10, 5, 22, 7, 14, 10, 14, 5, 18, 10, 18, 10, 10, 5, 28, 5, 10, 14, 15, 10, 20, 5, 14, 10, 20, 5, 26, 5, 10, 14, 14, 10, 20, 5

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OFFSET

1,1

LINKS

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

Index entries for sequences computed from exponents in factorization of n

FORMULA

Asymptotically: Sum_{k=1..n} a(k) = 2*C*n*log(n) + O(n*log(n)) with C = 1.1...

MATHEMATICA

a[n_] := 2 * DivisorSum[n, 2^MoebiusMu[#] &]; Array[a, 100] (* Amiram Eldar, Jun 04 2022 *)

PROG

(PARI) for(n=1, 100, print1(2*sumdiv(n, d, 2^moebius(d)), ", "))