A378981 a(n) = (A003961(n)-sigma(n)) mod (A003961(n)-2*n), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).

0, 0, 0, 0, 1, 0, 0, 1, 5, 0, 1, 17, 3, 4, 1, 1, 1, 36, 3, 21, 10, 3, 5, 75, 0, 0, 14, 0, 1, 33, 5, 1, 0, 3, 1, 134, 3, 2, 1, 99, 1, 69, 3, 4, 12, 0, 5, 281, 18, 7, 2, 6, 5, 255, 0, 177, 0, 3, 1, 147, 5, 2, 22, 1, 2, 51, 3, 10, 0, 87, 1, 480, 5, 9, 26, 12, 3, 87, 3, 381, 41, 3, 5, 271, 25, 9, 16, 171, 7, 291, 0, 16, 0, 15, 12

Offset: 1

Author

Antti Karttunen, Dec 12 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..32768
• Index entries for sequences related to prime indices in the factorization of n.
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A003961, A252748, A286385.

Cf. A378980 (positions of 0's), A349753 (positions of 0's at odd n).

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)));

Formula

a(n) = A286385(n) mod -A252748(n) = (A003961(n)-A000203(n)) mod ((2*n)-A003961(n)).