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A348513
Möbius transform of A048146, the sum of non-unitary divisors of n.
1
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 29 2021
STATUS
approved