A381403 a(n) is the mode of the multiset of bases and exponents (including exponents = 1) in the prime factorization of n (using smallest mode if multimodal).

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

Offset: 2

Author

Paolo Xausa, Feb 27 2025

Keywords

• nonn
• easy

Examples

			The prime factorization of 132 is 2^2*3^1*11^1, the multiset of these bases and exponents is {1, 1, 2, 2, 3, 11} and its smallest most frequent element is 1.
		

Links

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

Crossrefs

Cf. A035306, A381178, A381404.

Programs

Mathematica

A381403[n_] := Min[Commonest[Flatten[FactorInteger[n]]]];
Array[A381403, 100, 2]

Formula

a(p) = 1, for p prime.