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%I #29 Oct 15 2016 15:03:56
%S 1,511,713,11023,15553,43873,81079,323593,27923663,125093857,
%T 466572127,1108378657,2214217703,2871002911,3501195817,4107455887,
%U 4609840831,5066719081,5488711231,6331291231,9396536737
%N Numbers n such that 2^(sigma(n)-n) == 1 (mod n).
%C Terms are 1, 7*73, 23*31, 73*151, 103*151, 73*601, 89*911, 151*2143, ...
%C Obviously, there are no primes in this sequence and there are no squares of primes. n=p*q is in the sequence iff 2^(q+2) == 1 mod p and 2^(p+2) == 1 mod q. - _Robert Israel_, Sep 23 2016
%H Charles R Greathouse IV, <a href="/A277172/b277172.txt">Table of n, a(n) for n = 1..32</a>
%e 511 is a term because 2^(sigma(511)-511) == 1 (mod 511).
%o (PARI) is(n) = Mod(2, n)^(sigma(n)-n)==1;
%o (PARI) list(lim)=my(v=List([1]),t,s,n); lim\=1; forprime(p=3,sqrtint(lim\3), for(e=2,logint(lim,p), t=p^e; forstep(k=3,lim\t,2, if(k%p==0, next); s=(t*p-1)/(p-1)*sigma(k); n=t*k; if(Mod(2,n)^(s-n)==1, listput(v,n))))); forprime(p=3,lim\3, forstep(k=3,lim\p,2, if(k%p==0, next); s=(p+1)*sigma(k); n=p*k; if(Mod(2,n)^(s-n)==1, listput(v,n)))); Set(v) \\ _Charles R Greathouse IV_, Oct 04 2016
%Y Cf. A000203, A001065.
%K nonn
%O 1,2
%A _Altug Alkan_, Oct 03 2016
%E a(11)-a(21) from _Charles R Greathouse IV_, Oct 07 2016
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