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

1,1

Comments

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

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A007913, A254625.

Sequence in context: A293094 A233199 A232160 * A295590 A233220 A123478

Adjacent sequences: A260209 A260210 A260211 * A260213 A260214 A260215

Keyword

nonn

Author

Giovanni Resta, Jul 19 2015

Status

approved