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

2,1

Links

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

Formula

a(p) = p, for p prime.

Example

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.

Mathematica

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

Crossrefs

Second column of A381178.

Sequence in context: A332424 A293212 A157449 * A381404 A053139 A127705

Adjacent sequences: A381573 A381574 A381575 * A381577 A381578 A381579

Keyword

nonn,easy,new

Author

Paolo Xausa, Feb 28 2025

Status

approved