A392108 a(n) = smallest prime with exponent > 1 in the prime factorization of n, or 0 if no such prime exists.

0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 2, 0, 0, 0, 2, 0, 3, 0, 2, 0, 0, 0, 2, 5, 0, 3, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 2, 7, 5, 0, 2, 0, 3, 0, 2, 0, 0, 0, 2, 0, 0, 3, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 5, 2, 0, 0, 0, 2, 3, 0, 0, 2, 0, 0, 0, 2, 0, 3

Offset

1,4

Comments

First differs from A063958 and A392109 at n = 36.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

a(n) = min(A392066(n,1), A392066(n,2), ..., A392066(n,max(A056170(n),1))).

Example

a(6) = 0, since in the prime factorization of 6 = 2^1*3^1 no prime has exponent > 1.
a(35000) = 2, since the smallest prime in the prime factorization of 35000 = 2^3*5^4*7^1 having exponent > 1 is 5.

Maple

with(NumberTheory): a := proc(n) f := PrimeFactors(n/Radical(n)); ifelse(f = {}, 0, min(f)) end: seq(a(n), n = 1..90);  # Peter Luschny, Dec 31 2025

Mathematica

A392108[n_] := If[# == {}, 0, Min[#]] & [Select[FactorInteger[n], Last[#] > 1 &][[All, 1]]];
Array[A392108, 100]

Crossrefs

Cf. A056170, A063958, A080368, A392066, A392109.

Sequence in context: A263145 A057108 A349435 * A392066 A392109 A063958

Adjacent sequences: A392105 A392106 A392107 * A392109 A392110 A392111

Keyword

nonn

Author

Paolo Xausa, Dec 31 2025

Status

approved