A379489 a(n) = gcd(n,A003961(n))*gcd(sigma(n),A276086(n)) - gcd(n,A276086(n))*gcd(sigma(n),A003961(n)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.

0, 0, -1, 0, 5, 0, 1, 12, -2, -6, 5, 2, 1, 0, 15, 0, 17, 0, 9, -102, -1, 6, 5, 0, -24, 0, -5, 0, 29, 12, 1, 12, 3, 6, 35, 62, 1, 12, 11, 0, 41, -18, 1, 18, 15, 6, 5, 2, -6, -72, 3, 6, 17, 0, -3, -6, -5, 42, 29, 84, 1, 0, -19, 0, 35, 0, 1, 12, 3, -42, 17, 30, 1, 0, -65, 34, 59, 18, 9, -12, -2, 60, 41, 14, -3, 0, 15

Offset: 1

Author

Antti Karttunen, Jan 02 2025

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.
• Index entries for sequences related to primorial base.
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A003961, A276086, A379486 (positions of 0's), A379487, A379488.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A379489(n) = { my(s=sigma(n),x=A003961(n),y=A276086(n)); (gcd(n,x)*gcd(s,y))-(gcd(n,y)*gcd(s,x)); };

Formula

a(n) = A379487(n) - A379488(n) = A322361(n)*A324644(n) - A324198(n)*A342671(n).