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

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 *)

Prog

(PARI)
A003968(n) = {my(f=factor(n)); for (i=1, #f~, p= f[i, 1]; f[i, 1] = p*(p+1)^(f[i, 2]-1); f[i, 2] = 1); factorback(f); }
A348030(n) = (A003968(n)-n);

Crossrefs

Cf. A003959, A003968, A005117 (positions of zeros), A008683, A348029, A348036.

Sequence in context: A181502 A223154 A063698 * A287466 A288014 A179677

Adjacent sequences: A348027 A348028 A348029 * A348031 A348032 A348033

Keyword

nonn

Author

Antti Karttunen, Oct 19 2021

Status

approved