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%I #14 Nov 06 2016 19:53:45
%S 1,4,16,36,144,324,400,576,729,784,900,1764,1936,2304,2500,2704,2916,
%T 3600,4356,4624,5184,5776,6084,7056,8100,8464,9604,10000,10404,11664,
%U 12996,13456,14400,15376,15876,16384,17424,19044,20736,21904,22500,24336,25600,26244,26896,28224,29584,30276
%N Numbers n such that d(n) divides 2^n-1.
%C Sequence is infinite and all terms are squares. Square roots of terms are 1, 2, 4, 6, 12, 18, 20, 24, 27, 28, 30, 42, 44, 48, 50, 52, 54, 60, 66, 68, 72, 76, 78, 84, 90, 92, 98, 100, 102, 108, 114, 116, 120, 124, 126, 128, 132, 138, 144, ...
%H Chai Wah Wu, <a href="/A277285/b277285.txt">Table of n, a(n) for n = 1..10000</a>
%p a:= proc(n) option remember; local k;
%p for k from 1+`if`(n=1, 0, a(n-1))
%p while 0<>2&^k-1 mod numtheory[tau](k) do od; k
%p end:
%p seq(a(n), n=1..50); # _Alois P. Heinz_, Nov 06 2016
%t Select[Range[10^5], Divisible[2^# - 1, DivisorSigma[0, #]] &] (* _Michael De Vlieger_, Oct 10 2016 *)
%o (PARI) is(n) = (2^n-1) % numdiv(n) == 0;
%o (PARI) is(n)=Mod(2,numdiv(n))^n==1; \\ _Joerg Arndt_, Oct 09 2016
%o (Python)
%o from sympy import divisor_count
%o A277285_list = [1] + [j for j in (i**2 for i in range(1,10**4)) if pow(2,j,int(divisor_count(j))) == 1] # _Chai Wah Wu_, Nov 06 2016
%Y Cf. A000005, A000225, A277185.
%K nonn
%O 1,2
%A _Altug Alkan_, Oct 09 2016, following a suggestion from _Michel Marcus_ and _N. J. A. Sloane_
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