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%I #18 Aug 09 2015 14:53:00
%S 26999,122499,193599,599975,2206775,2620175,3501575,4798079,8278599,
%T 11631059,14242175,16956575,17578799,19048799,49061375,55504175,
%U 57354725,70963775,75271559,107499699,114930639,153536525,165887189,202729175,241430399,248688719,257552735,258969887,275089919
%N Nonsquarefree integers m such that, for prime p, if p^k | m then 1+p^k | 1+m.
%C The sequence is part of A056729.
%C All members are odd.
%e 26999 = 49*19*29 is in the list because 27000 is divisible by 8,50,20 and 30;
%e 193599 = 9*49*439 is in the list because 193600 is divisible by 4,10,8, 50,440.
%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[#+1, 1+PPDivs[#] ] ]== {0} &]
%Y Cf. A056729.
%K nonn
%O 1,1
%A _Emmanuel Vantieghem_, Jul 08 2013