

A242870


Numbers n such that (n^n2^2)/(n2) is an integer.


3



1, 3, 4, 6, 8, 14, 20, 22, 38, 44, 56, 62, 86, 102, 110, 128, 158, 164, 182, 222, 254, 296, 302, 326, 344, 380, 422, 470, 488, 502, 542, 590, 622, 662, 686, 758, 782, 822, 884, 902, 974, 1028, 1094, 1102, 1136, 1262, 1316, 1334, 1406, 1460, 1502, 1622, 1766, 1808
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OFFSET

1,2


COMMENTS

a(n) is even for all n > 2. 1 and 3 are members of this sequence because (n^n2^2)/(n2) becomes (2^2n^n) and (n^n2^2), respectively, which are both integers.
Given the term (n^nk^k)/(nk) (here, k=2), whenever k = 2^m for some m, there are significantly fewer data values within a given range of numbers. See A242871 for k=3.
These are also numbers n such that (2^nn^2)/(n2) is an integer.


LINKS



EXAMPLE

(4^42^2)/(42) = 252/2 = 126 is an integer. Thus, 4 is a member of this sequence.


MAPLE

filter:= proc(n) (n&^n  4) mod (n2) = 0 end proc;


MATHEMATICA

Join[{1}, Select[Range[3, 2000], IntegerQ[(#^#4)/(#2)]&]] (* Harvey P. Dale, Apr 24 2016 *)


PROG

(PARI) for(n=1, 2500, if(n!=2, s=(n^n2^2)/(n2); if(floor(s)==s, print(n))))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



