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A348508 a(n) = A003959(n) - 2*n, where A003959 is multiplicative with a(p^e) = (p+1)^e.

%I A348508 #17 Feb 18 2022 02:03:39
%S A348508 -1,-1,-2,1,-4,0,-6,11,-2,-2,-10,12,-12,-4,-6,49,-16,12,-18,14,-10,-8,
%T A348508 -22,60,-14,-10,10,16,-28,12,-30,179,-18,-14,-22,72,-36,-16,-22,82,
%U A348508 -40,12,-42,20,6,-20,-46,228,-34,8,-30,22,-52,84,-38,104,-34,-26,-58,96,-60,-28,2,601,-46,12,-66,26,-42,4,-70,288
%N A348508 a(n) = A003959(n) - 2*n, where A003959 is multiplicative with a(p^e) = (p+1)^e.
%H A348508 Antti Karttunen, <a href="/A348508/b348508.txt">Table of n, a(n) for n = 1..20000</a>
%F A348508 a(n) = A003959(n) - 2*n.
%F A348508 a(n) = A348507(n) - n.
%F A348508 a(n) = A348029(n) - A033879(n).
%F A348508 From _Antti Karttunen_, Dec 05 2021: (Start)
%F A348508 a(n) = A168036(n) + A348970(n).
%F A348508 For all n >= 1, a(A138636(n)) = 12.
%F A348508 (End)
%F A348508 a(p) = 1 - p if p prime. - _Bernard Schott_, Feb 17 2022
%t A348508 f[p_, e_] := (p + 1)^e; a[1] = -1; a[n_] := Times @@ f @@@ FactorInteger[n] - 2*n; Array[a, 100] (* _Amiram Eldar_, Oct 30 2021 *)
%o A348508 (PARI)
%o A348508 A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
%o A348508 A348508(n) = (A003959(n) - 2*n);
%Y A348508 Cf. A003959, A033879, A138636, A168036, A252748, A348029, A348970.
%K A348508 sign
%O A348508 1,3
%A A348508 _Antti Karttunen_, Oct 30 2021