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A379217 Quotient (A003961(k)-sigma(k)) / (2*k-A003961(k)) computed for those k for which this quotient is an integer, where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).

%I A379217 #14 Jan 09 2025 08:01:12
%S A379217 0,0,1,-2,-1,1,-3,18,9,-1,17,3,1,-35,-7,-15,57,-1,339,-381,3,-7,-969,
%T A379217 -1213,-1,3,3,-979,419,29,-42735,21,731232,3,1445,2809731,-4566981,
%U A379217 557,-19691,-1,5,544371,5,-475,-1784691,9051,176870849,808683,280791301,1803,-891775,-3679,-3733533,-444406677,731480523,275091
%N A379217 Quotient (A003961(k)-sigma(k)) / (2*k-A003961(k)) computed for those k for which this quotient is an integer, where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).
%C A379217 Terms in A378980 that correspond here with -1's are perfect numbers (A000396).
%H A379217 Antti Karttunen, <a href="/A379217/b379217.txt">Table of n, a(n) for n = 1..69</a> (based on b-file of A378980 computed by _Amiram Eldar_)
%H A379217 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%H A379217 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A379217 a(n) = A286385(A378980(n)) / A379216(n) = A286385(A378980(n)) / -A252748(A378980(n)).
%o A379217 (PARI)
%o A379217 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A379217 A378981(n) = ((A003961(n)-sigma(n))%((2*n)-A003961(n)));
%o A379217 is_A378980(n) = !A378981(n);
%o A379217 for(n=1,2^25,if(is_A378980(n),print1(((A003961(n)-sigma(n))/((2*n)-A003961(n))),", ")));
%Y A379217 Cf. A000396, A003961, A252748, A378980, A378981, A379216.
%K A379217 sign
%O A379217 1,4
%A A379217 _Antti Karttunen_, Dec 20 2024