A379488 a(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.

1, 3, 3, 1, 1, 3, 1, 3, 3, 15, 1, 1, 1, 3, 15, 1, 1, 3, 1, 105, 3, 3, 1, 15, 25, 3, 15, 1, 1, 3, 1, 9, 3, 3, 7, 1, 1, 3, 3, 45, 1, 21, 1, 3, 15, 3, 1, 1, 7, 75, 3, 1, 1, 15, 5, 21, 15, 3, 1, 21, 1, 3, 21, 1, 7, 3, 1, 9, 3, 105, 1, 15, 1, 3, 75, 1, 7, 3, 1, 15, 3, 3, 1, 7, 5, 3, 15, 9, 1, 3, 7, 3, 3, 3, 1, 9, 1, 147

Offset: 1

Author

Antti Karttunen, Jan 02 2025

Keywords

• nonn

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, A324198, A342671, A379486, A379487, A379489.

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); };
A379488(n) = { my(s=sigma(n),x=A003961(n),y=A276086(n)); (gcd(n,y)*gcd(s,x)); };

Formula

a(n) = A324198(n) * A342671(n).