A348030 - OEIS

A348030

a(n) = A003968(n) - n, where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).

0, 0, 0, 2, 0, 0, 0, 10, 3, 0, 0, 6, 0, 0, 0, 38, 0, 6, 0, 10, 0, 0, 0, 30, 5, 0, 21, 14, 0, 0, 0, 130, 0, 0, 0, 36, 0, 0, 0, 50, 0, 0, 0, 22, 15, 0, 0, 114, 7, 10, 0, 26, 0, 42, 0, 70, 0, 0, 0, 30, 0, 0, 21, 422, 0, 0, 0, 34, 0, 0, 0, 144, 0, 0, 15, 38, 0, 0, 0, 190, 111, 0, 0, 42, 0, 0, 0, 110, 0, 30, 0, 46

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OFFSET

1,4

COMMENTS

Möbius transform of A348029(n), which is A003959(n) - sigma(n).

LINKS

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

FORMULA

a(n) = A003968(n) - n.

a(n) = Sum_{d|n} A008683(n/d) * A348029(d).

MATHEMATICA

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