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A152000 a(n) is squarefree and such that for every prime p|a(n) and every prime q|p-1 then q|a(n) holds.

%I A152000 #21 Aug 24 2019 12:14:57
%S A152000 2,6,10,30,34,42,78,102,110,114,170,210,222,330,390,410,438,510,514,
%T A152000 546,570,582,654,714,798,930,978,1010,1110,1158,1218,1230,1326,1482,
%U A152000 1542,1554,1806,1830,1870,1938,2190,2310,2510,2530
%N A152000 a(n) is squarefree and such that for every prime p|a(n) and every prime q|p-1 then q|a(n) holds.
%C A152000 a(n) is a squarefree valid base.
%C A152000 Numbers m > 1 such that m equals A007947(A002618(m)). - _Jon Maiga_, Aug 08 2019
%H A152000 Jinyuan Wang, <a href="/A152000/b152000.txt">Table of n, a(n) for n = 1..10000</a>
%H A152000 J. Jimenez Urroz and J. Luis A.Yebra, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Yebra/yebra4.html">On the equation a^x=x mod b^n</a>, Journal of Integer Sequences, Vol. 12 (2009), Article 09.8.8.
%p A152000 A152000 := proc(n)
%p A152000     if n = 1 then
%p A152000         2;
%p A152000     else
%p A152000         for a from procname(n-1)+1 do
%p A152000             if issqrfree(a) then
%p A152000                 pdvs := numtheory[factorset](a) ;
%p A152000                 aworks := true;
%p A152000                 for p in numtheory[factorset](a) do
%p A152000                     for q in numtheory[factorset](p-1) do
%p A152000                         if a mod q = 0 then
%p A152000                             ;
%p A152000                         else
%p A152000                             aworks := false;
%p A152000                         end if;
%p A152000                     end do:
%p A152000                 end do:
%p A152000                 if aworks then
%p A152000                     return a;
%p A152000                 end if;
%p A152000             end if;
%p A152000         end do:
%p A152000     end if;
%p A152000 end proc: # _R. J. Mathar_, Jun 01 2013
%t A152000 rad[n_] := Times @@ (First@# & /@ FactorInteger@n);
%t A152000 Select[Range[2, 2530], # == rad[#*EulerPhi[#]] &] (* _Jon Maiga_, Aug 08 2019 *)
%o A152000 (PARI) is(m) = factorback(factorint(m*eulerphi(m))[, 1]) == m && m > 1; \\ _Jinyuan Wang_, Aug 08 2019
%Y A152000 Cf. A002618, A007947, A151999.
%K A152000 easy,nonn
%O A152000 1,1
%A A152000 J. Luis, A. Yebra and J. Jimenez Urroz, Nov 19 2008
%E A152000 Corrected and extended by _Michel Marcus_, Jun 01 2013