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%I #16 Sep 08 2022 08:46:06
%S 1,5,7,11,13,17,19,23,25,29,31,37,41,43,47,49,53,59,61,65,67,71,73,79,
%T 83,85,89,91,97,101,103,107,109,113,121,125,127,131,133,137,139,145,
%U 149,151,157,163,167,169,173,179,181,185,187,191,193,197,199,205,211
%N Numbers n such that p-1 does not divide n+1 for every prime divisor p of n.
%H Harvey P. Dale, <a href="/A231810/b231810.txt">Table of n, a(n) for n = 1..1000</a>
%t fa = FactorInteger; Gu[n_] := Union@Table[IntegerQ[(n + 1)/(fa[n][[i, 1]] - 1)], {i, Length[fa[n]]}]; Select[Range[20000], Gu[#] == {False} &]
%t Join[{1},Select[Range[2,300],NoneTrue[(#+1)/(FactorInteger[#][[All,1]]-1),IntegerQ]&]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 08 2019 *)
%o (PARI) isok(n) = {my(f=factor(n)[,1]); for (k=1, #f~, if (!((n+1) % (f[k]-1)), return(0));); return(1);} \\ _Michel Marcus_, Oct 02 2019
%o (Magma) [1] cat [k: k in [2..220]| #[p:p in PrimeDivisors(k)| IsIntegral((k+1)/(p-1))] eq 0]; // _Marius A. Burtea_, Oct 02 2019
%Y Cf. A231811.
%K nonn
%O 1,2
%A _José María Grau Ribas_, Jan 20 2014
%E Term 1 prepended by _Max Alekseyev_, Jan 20 2014
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