A379487 a(n) = gcd(n,A003961(n)) * gcd(sigma(n),A276086(n)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1), and A276086 is the primorial base exp-function.

1, 3, 2, 1, 6, 3, 2, 15, 1, 9, 6, 3, 2, 3, 30, 1, 18, 3, 10, 3, 2, 9, 6, 15, 1, 3, 10, 1, 30, 15, 2, 21, 6, 9, 42, 63, 2, 15, 14, 45, 42, 3, 2, 21, 30, 9, 6, 3, 1, 3, 6, 7, 18, 15, 2, 15, 10, 45, 30, 105, 2, 3, 2, 1, 42, 3, 2, 21, 6, 63, 18, 45, 2, 3, 10, 35, 66, 21, 10, 3, 1, 63, 42, 21, 2, 3, 30, 45, 90, 15, 14, 21

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, A322361, A324644, A379486, A379488, 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); };
A379487(n) = { my(s=sigma(n),x=A003961(n),y=A276086(n)); (gcd(n,x)*gcd(s,y)); };

Formula

a(n) = A322361(n) * A324644(n).