A348029 - OEIS

A348029

a(n) = A003959(n) - sigma(n), where A003959 is multiplicative with a(p^e) = (p+1)^e and sigma is the sum of divisors.

0, 0, 0, 2, 0, 0, 0, 12, 3, 0, 0, 8, 0, 0, 0, 50, 0, 9, 0, 12, 0, 0, 0, 48, 5, 0, 24, 16, 0, 0, 0, 180, 0, 0, 0, 53, 0, 0, 0, 72, 0, 0, 0, 24, 18, 0, 0, 200, 7, 15, 0, 28, 0, 72, 0, 96, 0, 0, 0, 48, 0, 0, 24, 602, 0, 0, 0, 36, 0, 0, 0, 237, 0, 0, 20, 40, 0, 0, 0, 300, 135, 0, 0, 64, 0, 0, 0, 144, 0, 54, 0, 48, 0

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OFFSET

1,4

COMMENTS

Inverse Möbius transform of A348030.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

FORMULA

a(n) = A003959(n) - A000203(n).

a(n) = Sum_{d|n} A348030(d).

MATHEMATICA

f[p_, e_] := (p + 1)^e; a[1] = 0; a[n_] := Times @@ f @@@ FactorInteger[n] - DivisorSigma[1, n]; Array[a, 100] (* Amiram Eldar, Oct 20 2021 *)