A381576 a(n) is the second element of the sorted multiset of bases and exponents (including exponents = 1) in the prime factorization of n.

2, 3, 2, 5, 1, 7, 3, 3, 1, 11, 2, 13, 1, 1, 4, 17, 2, 19, 2, 1, 1, 23, 2, 5, 1, 3, 2, 29, 1, 31, 5, 1, 1, 1, 2, 37, 1, 1, 2, 41, 1, 43, 2, 2, 1, 47, 2, 7, 2, 1, 2, 53, 2, 1, 2, 1, 1, 59, 1, 61, 1, 2, 6, 1, 1, 67, 2, 1, 1, 71, 2, 73, 1, 2, 2, 1, 1, 79, 2, 4, 1, 83, 1, 1, 1

Offset: 2

Author

Paolo Xausa, Feb 28 2025

Keywords

• nonn
• easy

Examples

			a(10) = 1 because the prime factorization of 10 is 2^1*5^1, the multiset of these bases and exponents is {1, 1, 2, 5} and its second element is 1.
a(18) = 2 because the prime factorization of 18 is 2^1*3^2, the multiset of these bases and exponents is {1, 2, 2, 3} and its second element is 2.
		

Links

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

Crossrefs

Second column of A381178.

Programs

Mathematica

A381576[n_] := Sort[Flatten[FactorInteger[n]]][[2]];
Array[A381576, 100, 2]

Formula

a(p) = p, for p prime.