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

1,1

Comments

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

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A076144.

Sequence in context: A179136 A249432 A331586 * A185534 A185526 A248458

Adjacent sequences: A077392 A077393 A077394 * A077396 A077397 A077398

Keyword

nonn

Author

Reinhard Zumkeller, Nov 04 2002

Status

approved