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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.
10
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
OFFSET
1,4
COMMENTS
Inverse Möbius transform of A348030.
LINKS
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 *)
PROG
(PARI)
A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A348029(n) = (A003959(n)-sigma(n));
CROSSREFS
Cf. A000203, A003959, A005117 (positions of zeros), A348030.
Sequence in context: A288014 A179677 A250397 * A224074 A136615 A283950
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 20 2021
STATUS
approved