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

%I A348513 #15 Feb 10 2022 18:58:49
%S A348513 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,
%T A348513 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,
%U A348513 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
%N A348513 Möbius transform of A048146, the sum of non-unitary divisors of n.
%H A348513 Antti Karttunen, <a href="/A348513/b348513.txt">Table of n, a(n) for n = 1..20000</a>
%F A348513 a(n) = n - A254503(n).
%F A348513 a(n) = Sum_{d|n} (A008683(n/d) * A048146(d)).
%t A348513 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 *)
%o A348513 (PARI)
%o A348513 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
%o A348513 A348513(n) = (n - A254503(n));
%Y A348513 Cf. A008683, A048146, A254503.
%K A348513 nonn
%O A348513 1,4
%A A348513 _Antti Karttunen_, Oct 29 2021