cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A245529 Numbers n such that 12^phi(n) == 1 (mod n^2), where phi(n) is Euler's totient function.

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%I A245529 #20 Jan 27 2020 15:44:02
%S A245529 2693,123653,1812389,2349407,12686723,201183431,332997529,3822485189,
%T A245529 6326953051,54520709801,224107337017,272603549005,541786979683,
%U A245529 1035893486219,1568751359119,4258039403323,5179467431095,10293952613977,29806275823261
%N A245529 Numbers n such that 12^phi(n) == 1 (mod n^2), where phi(n) is Euler's totient function.
%C A245529 a(8) > 10^9.
%C A245529 If a(n) is prime, it is in A111027.
%C A245529 a(20) > 10^14. - _Giovanni Resta_, Jan 27 2020
%H A245529 Takashi Agoh, Karl Dilcher and Ladislav Skula, <a href="http://dx.doi.org/10.1006/jnth.1997.2162">Fermat Quotients for Composite Moduli</a>, J. Number Theory, Volume 66, Issue 1 (1997), 29-50.
%p A245529 with(numtheory): A245529:=n->`if`( (12 &^ phi(n)-1) mod n^2 = 0, n, NULL): seq(A245529(n), n=2..10^4); # _Wesley Ivan Hurt_, Jul 26 2014
%t A245529 Select[Range[10^5], PowerMod[12, EulerPhi[#], #^2] == 1 &] (* _Alonso del Arte_, Jul 27 2014 *)
%o A245529 (PARI) for(n=2, 1e9, if(Mod(12, n^2)^(eulerphi(n))==1, print1(n, ", ")))
%Y A245529 Cf. A000010, A077816, A242958, A242959, A242960, A111027.
%K A245529 nonn,more
%O A245529 1,1
%A A245529 _Felix Fröhlich_, Jul 25 2014
%E A245529 a(8)-a(12) from _Giovanni Resta_, Jan 24 2020
%E A245529 a(13)-a(19) from _Giovanni Resta_, Jan 27 2020