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%I #8 Nov 04 2013 11:07:58
%S 7,17,19,26,31,41,49,53,55,65,71,76,97,109,127,129,161,191,197,199,
%T 209,239,241,251,271,289,295,351,391,401,433,449,485,511,575,577,626,
%U 647,649,685,701,703,721,727,799,811,881,883,901,967,989,1025,1055,1079
%N Numbers n such that there exists a smaller number k such that k^2-1 has exactly the same set of distinct prime divisors as n^2-1
%F a(1)=7 because set of prime divisors of 7^2-1 is the same as for 5^2-1. The set is {2,3}.
%t aa = {}; bb = {}; Do[k = n^2 - 1; c = FactorInteger[k]; b = {}; Do[AppendTo[b, c[[m]][[1]]], {m, 1, Length[c]}]; If[Position[aa, b] != {}, AppendTo[bb, n], AppendTo[aa, b]], {n, 2, 10000}]; bb (*Artur Jasinski*)
%o (PARI) isok(n) = {pfs = factor(n^2-1)[,1]; for (k = 2, n-1, if (factor(k^2-1)[,1] == pfs, return (1));); return (0);} \\ _Michel Marcus_, Nov 04 2013
%Y Cf. A175902 (for corresponding k).
%K nonn
%O 1,1
%A _Artur Jasinski_, Oct 11 2010
%E Edited by _N. J. A. Sloane_, Oct 14 2010
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