A249739 The smallest prime whose square divides n, 1 if n is squarefree.

1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 5, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 7, 5, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 5, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 7, 3, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2

Offset: 1

Author

Antti Karttunen, Nov 04 2014

Keywords

• nonn

Comments

A249740 gives the corresponding largest prime.

If n belongs to A013929, then a(n)>1. - Robert G. Wilson v, Nov 16 2016

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003557, A005117, A013929, A020639, A046027, A249717.

Differs from A071773 and A249740 for the first time at n=36, where a(36) = 2, while A249740(36) = 3 and A071773(36) = 6.

Programs

Mathematica

Table[If[SquareFreeQ@ n, 1, p = 2; While[! Divisible[n, p^2], p = NextPrime@ p]; p], {n, 120}] (* Michael De Vlieger, Nov 15 2016 *)

PARI

a(n) = {f = factor(n/core(n)); vsq = select(x->((x%2) == 0), f[,2], 1); if (#vsq, f[vsq[1], 1], 1);} \\ Michel Marcus, Mar 11 2017

Scheme

(define (A249739 n) (let loop ((n n) (p (A020639 n))) (cond ((= 1 n) n) ((zero? (modulo n (* p p))) p) (else (loop (/ n p) (A020639 (/ n p)))))))

Formula

a(n) = A020639(A003557(n)). - Amiram Eldar, Feb 11 2021