%I #10 Oct 29 2021 07:19:53

%S 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,

%T 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,

%U 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

%N a(n) = A003959(n) - sigma(n), where A003959 is multiplicative with a(p^e) = (p+1)^e and sigma is the sum of divisors.

%C Inverse Möbius transform of A348030.

%H Antti Karttunen, <a href="/A348029/b348029.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = A003959(n) - A000203(n).

%F a(n) = Sum_{d|n} A348030(d).

%t 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 *)

%o (PARI)

%o A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };

%o A348029(n) = (A003959(n)-sigma(n));

%Y Cf. A000203, A003959, A005117 (positions of zeros), A348030.

%K nonn

%O 1,4

%A _Antti Karttunen_, Oct 20 2021