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%I #24 Oct 06 2021 12:04:19
%S 1,5,17,257,46657,65537,148997,67371265,405458497,1370776577,
%T 3497539601,4294967297,80542440001,422240040001,1911029760001,
%U 139251776898727937,286245437364810001,6017402415698251777,18446744073709551617
%N Numbers of the form n^2+1 that divide 4^n-1.
%C Corresponding values of n are given by A273870(k)-1 for k>=1.
%C Contains Fermat numbers (A000215) greater than 3.
%C Also, numbers of the form n^2+1 that divide (4^k)^n-1 for all k >= 0.
%C a(20) > 4*10^24, if it exists. - _Giovanni Resta_, Feb 26 2020
%F a(n) = (A273870(n)-1)^2+1.
%e 17 = 4^2+1 is a term because divides 4^4-1; 255 / 17 = 15.
%o (PARI) is(n) = ceil(sqrt(n-1))==sqrtint(n-1) && Mod(4, n)^(sqrtint(n))==1
%o for(n=0, 1e12, if(is(n^2+1), print1(n^2+1, ", "))) \\ _Felix Fröhlich_, Jun 06 2016
%Y Subsequence of A002522 (numbers of the form n^2+1).
%Y Prime terms are in A274000.
%Y Cf. A000215, A002522, A273870, A273871, A274000.
%K nonn,more
%O 1,2
%A _Jaroslav Krizek_, Jun 06 2016
%E a(16)-a(19) from _Lars Blomberg_, Aug 10 2016
%E Edited by _Max Alekseyev_, Apr 30 2018