A379216 Difference 2*k - A003961(k) computed for k for which this difference divides difference (A003961(k)-sigma(k)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).

1, 1, 1, -1, -3, 3, -1, 1, 1, -43, 1, 5, 19, -1, -7, -5, 1, -2005, 1, -1, 149, -193, -1, -3, -79243, 1243, 1253, -7, 51, 581, -1, 3093, 1, 155491, 919, 1, -1, 15833, -877, -4295498497, 5129369, 31, 5779339, -69187, -29, 6745, 1, 181, 1, 69197, -397, -117433, -101, -1, 1, 2759, 1, -29479, 1, -5626288431709, 29669, -1, -132239, -1, -1, 14591, -2267959, -3187, 787250461

Offset: 1

Author

Antti Karttunen, Dec 20 2024

Keywords

• sign

Comments

Among the initial 69 terms, there are eleven +1's and eleven -1's. The former correspond in A378980 with those of its terms that are in A048674 (1, 2, 3, 25, 26, 33, 93, 1034, ...), while the latter here correspond in A378980 with those of its terms that are in A348514 (4, 10, 57, 1054, 2626, ...).

Links

• Index entries for sequences related to prime indices in the factorization of n.
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A003961, A048674, A252748, A348514, A378980, A378981, A379217.

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((2*n)-A003961(n),", ")));

Formula

a(n) = -A252748(A378980(n)).