# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a225711
Showing 1-1 of 1

%I A225711 #15 Jul 18 2022 23:53:55
%S A225711 385,2737,6061,6721,17641,24769,25201,31521,34561,49105,66385,76609,
%T A225711 79401,113221,136081,180481,194833,199801,254881,268801,311905,321937,
%U A225711 328321,362881,436645,469201,506521,545905,547561,558145,628705,642505,649153,778261,884305
%N A225711 Composite squarefree numbers n such that p(i)+1 divides n-1, where p(i) are the prime factors of n.
%H A225711 Paolo P. Lava, <a href="/A225711/b225711.txt">Table of n, a(n) for n = 1..150</a>
%H A225711 Qi-Yang Zheng, <a href="https://arxiv.org/abs/2207.08641">There are infinitely many (-1,1)-Carmichael numbers</a>, arXiv:2207.08641 [math.NT], 2022.
%e A225711 Prime factors of 24769 are 17, 31 and 47. We have that (24769-1)/(17+1) = 1376, (24769-1)/(31+1) = 774 and (24769-1)/(47+1) = 516.
%p A225711 with(numtheory); A225711:=proc(i,j) local c, d, n, ok, p, t;
%p A225711 for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;
%p A225711 for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;
%p A225711 if  not type((n+j)/(p[d][1]-j),integer) then ok:=0; break; fi; od;
%p A225711 if ok=1 then print(n); fi; fi; od; end: A225711(10^9,-1);
%t A225711 t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n - 1, p + 1]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* _T. D. Noe_, May 17 2013 *)
%Y A225711 Cf. A208728, A225702-A225710, A225712-A225720.
%K A225711 nonn
%O A225711 1,1
%A A225711 _Paolo P. Lava_, May 13 2013

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE