A077395 Lesser of two successive squarefree numbers whose product is not squarefree.

174, 422, 474, 602, 831, 843, 930, 1074, 1182, 1322, 1374, 1443, 1518, 1623, 1803, 1974, 2006, 2022, 2222, 2274, 2298, 2522, 2526, 2595, 2694, 2870, 2874, 3122, 3210, 3282, 3423, 3478, 3574, 3702, 3770, 3774, 4022, 4074, 4202, 4323, 4359, 4458, 4474

Offset: 1

Author

Reinhard Zumkeller, Nov 04 2002

Keywords

• nonn

Comments

Squarefree numbers b(m) = A005117(m) such that gcd(b(m),b(m+1)) > 1. - Thomas Ordowski, Aug 15 2015

Examples

			A005117(106)*A005117(107) = 174*177 = (2*3*29)*(3*59) is not squarefree, therefore 174 is a term.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A076144.

Programs

Maple

SF:= select(numtheory:-issqrfree,[$1..10000]):
map(t -> if igcd(SF[t],SF[t+1])>1 then SF[t] else NULL fi, [$1..nops(SF)-1]); # Robert Israel, Aug 16 2015

Mathematica

Transpose[Select[Partition[Select[Range[5000],SquareFreeQ],2,1], !SquareFreeQ[ Times@@#]&]][[1]] (* Harvey P. Dale, Dec 14 2012 *)

PARI

lista(nn) = {last = 2; for (n=3, nn, if (issquarefree(n), if (! issquarefree(last*n), print1(last, ", ")); last = n;););} \\ Michel Marcus, Aug 17 2015

Formula

Conjecture: lim_{n->oo} n/a(n) > 0. - Thomas Ordowski and Robert Israel, Aug 18 2015