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).

0, 0, 1, -2, -1, 1, -3, 18, 9, -1, 17, 3, 1, -35, -7, -15, 57, -1, 339, -381, 3, -7, -969, -1213, -1, 3, 3, -979, 419, 29, -42735, 21, 731232, 3, 1445, 2809731, -4566981, 557, -19691, -1, 5, 544371, 5, -475, -1784691, 9051, 176870849, 808683, 280791301, 1803, -891775, -3679, -3733533, -444406677, 731480523, 275091

Offset: 1

Author

Antti Karttunen, Dec 20 2024

Keywords

• sign

Comments

Terms in A378980 that correspond here with -1's are perfect numbers (A000396).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..69 (based on b-file of A378980 computed by _Amiram Eldar_)
• Index entries for sequences related to prime indices in the factorization of n.
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000396, A003961, A252748, A378980, A378981, A379216.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A378981(n) = ((A003961(n)-sigma(n))%((2*n)-A003961(n)));
is_A378980(n) = !A378981(n);
for(n=1,2^25,if(is_A378980(n),print1(((A003961(n)-sigma(n))/((2*n)-A003961(n))),", ")));

Formula

a(n) = A286385(A378980(n)) / A379216(n) = A286385(A378980(n)) / -A252748(A378980(n)).