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A225814 Nonsquarefree integers m such that, for prime p, if p^k|m then 2+p^k|2+m. 1

%I

%S 44770,825550,27354103,123572293,140307550,148925950,213663175,

%T 375064963,1002265990,1579248097,2953883023,3985833850,4716952513,

%U 4871428198,4929024175,9067177798

%N Nonsquarefree integers m such that, for prime p, if p^k|m then 2+p^k|2+m.

%C Squarefree integers m such that p|m implies 2+p|2+m are in A029562.

%C No element in the sequence is divisible by 4.

%H Giovanni Resta, <a href="/A225814/b225814.txt">Table of n, a(n) for n = 1..50</a>

%e 44770 = 2*5*37*11^2 is in the list because 44772 is divisible by 4, 7, 39, 13 and 123.

%e 27354103 = 151*3697*7^2 is in the list because 27354105 is divisible by 153, 3699, 9 and 51.

%t PPDivs[m_Integer]:=Module[{f=FactorInteger[m]}, Flatten[Table[First[f[[i]]]^Range[Last[f[[i]]]], {i, 1, Length[f]}]]]; Select[Select[ Range[1000000], !SquareFreeQ[#]&], Union[ Mod[#+2, 2+PPDivs[#] ] ]== {0} &]

%K nonn

%O 1,1

%A _Emmanuel Vantieghem_, Jul 29 2013

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Last modified May 25 05:45 EDT 2022. Contains 354048 sequences. (Running on oeis4.)