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

1,2

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).

Formula

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

Prog

(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)); };

Crossrefs

Cf. A000203, A003961, A276086, A322361, A324644, A379486, A379488, A379489.

Sequence in context: A361470 A134199 A323417 * A102189 A031252 A208152

Adjacent sequences: A379484 A379485 A379486 * A379488 A379489 A379490

Keyword

nonn

Author

Antti Karttunen, Jan 02 2025

Status

approved