A378982 a(n) = (A003961(n)-(1+sigma(n))) mod (A003961(n)-2*n), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).

0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 16, 2, 3, 0, 0, 0, 35, 2, 20, 9, 2, 4, 74, 0, 0, 13, 42, 0, 32, 4, 0, 0, 2, 0, 133, 2, 1, 0, 98, 0, 68, 2, 3, 11, 4, 4, 280, 17, 6, 1, 5, 4, 254, 18, 176, 0, 2, 0, 146, 4, 1, 21, 0, 1, 50, 2, 9, 6, 86, 0, 479, 4, 8, 25, 11, 2, 86, 2, 380, 40, 2, 4, 270, 24, 8, 15, 170, 6, 290, 4, 15

Offset: 1

Author

Antti Karttunen, Dec 13 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, A378983 (positions of 0's).

Cf. also A378981.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A378982(n) = ((A003961(n)-(sigma(n)+1))%((2*n)-A003961(n)));

Formula

a(n) = (A286385(n)-1) mod A252748(n).