A277172 Numbers n such that 2^(sigma(n)-n) == 1 (mod n).

1, 511, 713, 11023, 15553, 43873, 81079, 323593, 27923663, 125093857, 466572127, 1108378657, 2214217703, 2871002911, 3501195817, 4107455887, 4609840831, 5066719081, 5488711231, 6331291231, 9396536737

Offset

1,2

Comments

Terms are 1, 7*73, 23*31, 73*151, 103*151, 73*601, 89*911, 151*2143, ...

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

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..32

Example

511 is a term because 2^(sigma(511)-511) == 1 (mod 511).

Prog

(PARI) is(n) = Mod(2, n)^(sigma(n)-n)==1;
(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

Crossrefs

Cf. A000203, A001065.

Sequence in context: A242218 A051985 A103206 * A023691 A045118 A043451

Adjacent sequences: A277169 A277170 A277171 * A277173 A277174 A277175

Keyword

nonn

Author

Altug Alkan, Oct 03 2016

Extensions

a(11)-a(21) from Charles R Greathouse IV, Oct 07 2016

Status

approved