A260212 Integers n such that core(n), core(n+1), core(n+2) are smaller than n^(1/2) where core(n) is A007913(n), the squarefree part of n.

48, 9800, 31211, 32798, 48373, 59534, 63000, 118579, 373827, 488187, 629693, 830464, 1294298, 3815174, 8388223, 9235520, 9516680, 9841094, 11121382, 12708359, 14325848, 15407171, 18966023, 19890624, 24737542, 28140000, 29320000, 29445038, 34032190, 38033406

Offset: 1

Author

Giovanni Resta, Jul 19 2015

Keywords

• nonn

Comments

Up to 10^12, the only quadruplet starts at 160150258573.

Examples

			48 is a term since core(48) = 3, core(49) = 1 and core(50) = 2 are all smaller than the square root of 48.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..461 (terms < 10^12)

Crossrefs

Cf. A007913, A254625.

Programs

Mathematica

core[n_] := Times@@ ((#[[1]] ^ Mod[#[[2]], 2])& /@ FactorInteger@ n); Select[ Range[10^6], core[#]^2 < # && core[#+1]^2 < # && core[#+2]^2 < # &]