A306671 a(n) = gcd(tau(n), pod(n)) where tau(k) = the number of the divisors of k (A000005) and pod(k) = the product of the divisors of k (A007955).

1, 2, 1, 1, 1, 4, 1, 4, 3, 4, 1, 6, 1, 4, 1, 1, 1, 6, 1, 2, 1, 4, 1, 8, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 9, 1, 4, 1, 8, 1, 8, 1, 2, 3, 4, 1, 2, 1, 2, 1, 2, 1, 8, 1, 8, 1, 4, 1, 12, 1, 4, 3, 1, 1, 8, 1, 2, 1, 8, 1, 12, 1, 4, 3, 2, 1, 8, 1, 10, 1, 4, 1, 12, 1, 4

Offset: 1

Author

Jaroslav Krizek, Mar 04 2019

Keywords

• nonn

Comments

Sequence of the smallest numbers k such that a(k) = n: 1, 2, 9, 6, 400, 12, 3136, 24, 36, 80, 123904, 60, 692224, 448, 2025, 120, ...

Examples

			For n=6: a(6) = gcd(tau(6), pod(6)) = gcd(4, 36) = 4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000005, A007955, A009205, A046642.

Programs

Magma

[GCD(NumberOfDivisors(n), &*[d: d in Divisors(n)]): n in [1.. 100]]

PARI

a(n) = gcd(numdiv(n), vecprod(divisors(n))); \\ Michel Marcus, Mar 04 2019

Formula

a(n) = 1 for numbers in A046642.

a(n) = tau(n) for numbers in A120736.