A379229 Difference A003961(k)-(2*k) computed for the natural numbers k for which k and A003961(k) are relatively prime, where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).

-1, -1, -1, 1, -3, -3, 11, 7, 1, -9, -9, 5, 49, -15, -15, 23, 13, -5, -17, -1, -1, 71, 43, -27, -25, 179, -1, -11, -33, -7, 7, 109, -39, -39, 29, -5, -41, 23, 47, -7, 49, -47, -19, 185, 1, -23, -57, -55, -13, 149, 601, -11, -63, 35, 7, -69, -67, -25, 55, -75, 407, 463, -35, -77, -37, -31, -19, 175, -81, 5, 77, -1

Offset: 1

Author

Antti Karttunen, Dec 23 2024

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to prime indices in the factorization of n.

Crossrefs

Cf. A003961, A252748, A319630.

Cf. also A379230.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A252748(n) = (A003961(n) - (2*n));
is_A319630(n) = (1==gcd(n,A003961(n)));
k=0; n=0; while(k<200, n++; if(is_A319630(n), print1(A252748(n),", ")));

Formula

a(n) = A252748(A319630(n)).