A351445 - OEIS

%I #15 Feb 12 2022 20:29:53

%S 0,1,-1,5,-2,0,-5,7,8,0,-8,4,-6,-4,-6,29,-12,20,-14,8,-11,-6,-20,6,14,

%T 0,-4,0,-20,-4,-29,23,-18,-8,-22,68,-18,-10,-18,12,-28,-10,-32,2,8,

%U -18,-44,28,0,44,-28,24,-44,0,-36,2,-32,-12,-50,4,-30,-28,-12,125,-36,-16,-50,8,-42,-20,-66,92,-36,0

%N a(n) = A003958(sigma(n)) - A003958(n), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.

%H Antti Karttunen, <a href="/A351445/b351445.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A351442(n) - A003958(n) = A351444(n) - n.

%o (PARI)

%o A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };

%o A351445(n) = (A003958(sigma(n)) - A003958(n));

%Y Cf. A000203, A003958, A351442, A351444, A351457 [= a(A003961(n))].

%Y Cf. A351446 (positions of zeros), A351443 (odd terms there).

%Y Cf. also A348736.

%K sign

%O 1,4

%A _Antti Karttunen_, Feb 12 2022