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A280149 Numbers k such that 3^k - 2^k is not squarefree.

%I A280149 #33 Jun 30 2023 03:56:31
%S A280149 10,11,20,22,30,33,40,42,44,50,52,55,57,60,66,70,77,80,84,88,90,99,
%T A280149 100,104,110,114,120,121,126,130,132,140,143,150,154,156,160,165,168,
%U A280149 170,171,176,180,187,190,198,200,203,208,209,210,220,228,230,231,240,242,250,252,253,260,264,270,272,275,280,285
%N A280149 Numbers k such that 3^k - 2^k is not squarefree.
%C A280149 Primitive members (not multiples of earlier terms) are 10, 11, 42, 52, 57, 203, 272, 497, .... - _Juri-Stepan Gerasimov_ and _Charles R Greathouse IV_, Dec 27 2016
%C A280149 From _Robert Israel_, Dec 27 2016: (Start)
%C A280149 Numbers divisible by the order of 3/2 mod p^2 for some prime p > 3.
%C A280149 Includes numbers divisible by p^2-p for some prime p > 3.
%C A280149 If k is a member, then so are all multiples of k. (End)
%H A280149 Charles R Greathouse IV and Amiram Eldar, <a href="/A280149/b280149.txt">Table of n, a(n) for n = 1..134</a> (terms 1..127 from Charles R Greathouse IV)
%e A280149 10 is in this sequence because 3^10 - 2^10 = 58025 = 5^2*11*211.
%t A280149 Select[Range@ 120, ! SquareFreeQ[3^# - 2^#] &] (* _Michael De Vlieger_, Dec 27 2016 *)
%o A280149 (Magma) [n: n in [1..156] | not IsSquarefree(3^n-2^n)];
%o A280149 (PARI) is(n)=issquarefree(3^n-2^n)==0 \\ _Charles R Greathouse IV_, Dec 27 2016
%Y A280149 Cf. A001047, A005117, A013929, A049094, A057468, A082869, A282688, A282689.
%K A280149 nonn
%O A280149 1,1
%A A280149 _Juri-Stepan Gerasimov_, Dec 27 2016
%E A280149 More terms from _Charles R Greathouse IV_, Dec 27 2016