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

2,3

Links

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

Formula

a(p) = 1, for p prime.

Example

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.

Mathematica

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

Crossrefs

Cf. A035306, A381178, A381404.

Sequence in context: A358260 A368978 A381613 * A255326 A085424 A088737

Adjacent sequences: A381400 A381401 A381402 * A381404 A381405 A381406

Keyword

nonn,easy,new

Author

Paolo Xausa, Feb 27 2025

Status

approved