A381404 a(n) is the mode of the multiset of bases and exponents (including exponents = 1) in the prime factorization of n (using largest mode if multimodal).

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

Offset

2,1

Links

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

Formula

a(p) = p, 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 largest most frequent element is 2.

Mathematica

A381404[n_] := Max[Commonest[Flatten[FactorInteger[n]]]];
Array[A381404, 100, 2]

Crossrefs

Cf. A035306, A381178, A381403.

Cf. A000040 (fixed points).

Sequence in context: A293212 A157449 A381576 * A053139 A127705 A124386

Adjacent sequences: A381401 A381402 A381403 * A381405 A381406 A381407

Keyword

nonn,easy,new

Author

Paolo Xausa, Feb 27 2025

Status

approved