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

1,2

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) = A324198(n) * A342671(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); };
A379488(n) = { my(s=sigma(n), x=A003961(n), y=A276086(n)); (gcd(n, y)*gcd(s, x)); };

Crossrefs

Cf. A000203, A003961, A276086, A324198, A342671, A379486, A379487, A379489.

Sequence in context: A365213 A126717 A124039 * A350617 A337743 A335624

Adjacent sequences: A379485 A379486 A379487 * A379489 A379490 A379491

Keyword

nonn

Author

Antti Karttunen, Jan 02 2025

Status

approved