A069187 Numbers k such that core(k) = ceiling(sqrt(k)) where core(k) is the squarefree part of k (the smallest integer such that k*core(k) is a square).

1, 2, 20, 90, 272, 650, 1332, 4160, 6642, 10100, 14762, 20880, 28730, 38612, 50850, 65792, 83810, 130682, 160400, 194922, 234740, 280370, 332352, 391250, 457652, 532170, 615440, 708122, 810900, 924482, 1187010, 1337492, 1501850, 1680912, 1875530, 2314962, 2561600

Offset: 1

Author

Benoit Cloitre, Apr 14 2002

Keywords

• nonn

Comments

Conjecture: sequence is A071253 minus those entries of A071253 that have their index in A049532, i.e., a(n) is of form n^2*(n^2+1) for all n not in A049532. - Ralf Stephan, Aug 18 2004

Links

• Amiram Eldar, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A007913, A049532, A071253.

Programs

Mathematica

core[n_] := Times @@ Apply[ Power, {#[[1]], Mod[#[[2]], 2]}& /@ FactorInteger[n], {1}]; Select[Range[500000], core[#] == Ceiling[Sqrt[#]]&] (* Jean-François Alcover, Jul 26 2011 *)

Extensions

More terms from Amiram Eldar, Sep 10 2020