A348513 - OEIS

%I #15 Feb 10 2022 18:58:49

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

%H Antti Karttunen, <a href="/A348513/b348513.txt">Table of n, a(n) for n = 1..20000</a>

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

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

%t 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 (PARI)

%o 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(n) = (n - A254503(n));

%Y Cf. A008683, A048146, A254503.

%K nonn

%O 1,4

%A _Antti Karttunen_, Oct 29 2021