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A348030
a(n) = A003968(n) - n, where A003968 is multiplicative with a(p^e) = p*(p+1)^(e-1).
4
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 19 2021
STATUS
approved