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A348732 a(n) = A003959(n) - A034448(n), where A003959 is multiplicative with a(p^e) = (p+1)^e and A034448 (usigma) is multiplicative with a(p^e) = (p^e)+1.

%I A348732 #13 Nov 05 2021 22:29:03
%S A348732 0,0,0,4,0,0,0,18,6,0,0,16,0,0,0,64,0,18,0,24,0,0,0,72,10,0,36,32,0,0,
%T A348732 0,210,0,0,0,94,0,0,0,108,0,0,0,48,36,0,0,256,14,30,0,56,0,108,0,144,
%U A348732 0,0,0,96,0,0,48,664,0,0,0,72,0,0,0,342,0,0,40,80,0,0,0,384,174,0,0,128,0,0,0,216,0,108
%N A348732 a(n) = A003959(n) - A034448(n), where A003959 is multiplicative with a(p^e) = (p+1)^e and A034448 (usigma) is multiplicative with a(p^e) = (p^e)+1.
%H A348732 Antti Karttunen, <a href="/A348732/b348732.txt">Table of n, a(n) for n = 1..21125</a>
%F A348732 a(n) = A003959(n) - A034448(n).
%F A348732 a(n) = A348507(n) - A034460(n).
%F A348732 a(n) = A048146(n) + A348029(n).
%t A348732 f1[p_, e_] := (p + 1)^e; f2[p_, e_] := p^e + 1; a[n_] := Times @@ f1 @@@ (f = FactorInteger[n]) - Times @@ f2 @@@ f; Array[a, 100] (* _Amiram Eldar_, Oct 31 2021 *)
%o A348732 (PARI)
%o A348732 A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
%o A348732 A034448(n) = { my(f = factor(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
%o A348732 A348732(n) = (A003959(n)-A034448(n));
%Y A348732 Cf. A003959, A005117 (positions of zeros), A034448, A034460, A048146, A348029, A348507.
%K A348732 nonn
%O A348732 1,4
%A A348732 _Antti Karttunen_, Oct 31 2021