A381204 a(n) is the gcd of the elements of the set of bases and exponents in the prime factorization of n.

1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 2

Author

Paolo Xausa, Feb 17 2025

Keywords

• nonn
• easy

Comments

The positions of terms > 1 are given by A368107.

Examples

			a(16) = 2 because 16 = 2^4, the set of these bases and exponents is {2, 4} and gcd(2, 4) = 2.
a(19683) = 3 because 19683 = 3^9, the set of these bases and exponents is {3, 9} and gcd(3, 9) = 3.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A368107, A381201, A381202, A381203, A381205.

Programs

Mathematica

A381204[n_] := GCD @@ Flatten[FactorInteger[n]];
Array[A381204, 100 ,2]

PARI

a(n) = my(f=factor(n)); gcd(setunion(Set(f[,1]), Set(f[,2]))); \\ Michel Marcus, Feb 18 2025