A348513 Möbius transform of A048146, the sum of non-unitary divisors of n.

0, 0, 0, 2, 0, 0, 0, 4, 3, 0, 0, 6, 0, 0, 0, 8, 0, 6, 0, 10, 0, 0, 0, 12, 5, 0, 9, 14, 0, 0, 0, 16, 0, 0, 0, 24, 0, 0, 0, 20, 0, 0, 0, 22, 15, 0, 0, 24, 7, 10, 0, 26, 0, 18, 0, 28, 0, 0, 0, 30, 0, 0, 21, 32, 0, 0, 0, 34, 0, 0, 0, 48, 0, 0, 15, 38, 0, 0, 0, 40, 27, 0, 0, 42, 0, 0, 0, 44, 0, 30, 0, 46, 0, 0, 0, 48, 0, 14

Offset

1,4

Links

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

Formula

a(n) = n - A254503(n).

a(n) = Sum_{d|n} (A008683(n/d) * A048146(d)).

Mathematica

nusigma[1] = 0; nusigma[n_] := DivisorSigma[1, n] - Times @@ (1 + Power @@@ FactorInteger[n]); a[n_] := DivisorSum[n, MoebiusMu[n/#]*nusigma[#] &]; Array[a, 100] (* Amiram Eldar, Oct 30 2021 *)

Prog

(PARI)
A254503(n) = {my(f = factor(n)); for (i=1, #f~, if ((e=f[i, 2]) > 1, f[i, 1] = eulerphi(f[i, 1]^e); f[i, 2] = 1); ); factorback(f); }; \\ From A254503
A348513(n) = (n - A254503(n));

Crossrefs

Cf. A008683, A048146, A254503.

Sequence in context: A129183 A280292 A181566 * A110173 A328820 A259863

Adjacent sequences: A348510 A348511 A348512 * A348514 A348515 A348516

Keyword

nonn

Author

Antti Karttunen, Oct 29 2021

Status

approved