A392109 a(n) = largest 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, 3, 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, 3, 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 A392108 at n = 36.

Links

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

Formula

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

a(n) = max(0, factors(n/rad(n))), where factors(n) is the set of prime factors of n. - Peter Luschny, Dec 31 2025

Example

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

Maple

with(NumberTheory): a := n -> max(0, PrimeFactors(n/Radical(n))):
seq(a(n), n = 1..90); # Peter Luschny, Dec 31 2025

Mathematica

A392109[n_] := Max[Select[FactorInteger[n], Last[#] > 1 &][[All, 1]], 0];
Array[A392109, 100]

Crossrefs

Cf. A027748, A056170, A063958, A080367, A392066, A392108.

Sequence in context: A349435 A392108 A392066 * A063958 A349434 A126164

Adjacent sequences: A392106 A392107 A392108 * A392110 A392111 A392112

Keyword

nonn

Author

Paolo Xausa, Dec 31 2025

Status

approved