A056729 If p | n, then p+1 | n+1 for composite n.

8, 27, 32, 63, 125, 128, 243, 275, 343, 399, 512, 567, 575, 935, 1127, 1331, 1539, 2015, 2048, 2187, 2197, 2303, 2783, 2915, 3087, 3125, 4563, 4913, 4991, 5103, 5719, 5831, 6399, 6859, 6875, 6929, 7055, 7139, 7625, 8192, 8855, 12167, 12719, 14027

Offset: 1

Author

Robert G. Wilson v, Aug 31 2000

Keywords

• nonn

Comments

The Lucas-Carmichael numbers (A006972) are a subset.

Contains p^(2k+1) for any prime p, since (x+1) | (x^n + 1) when n is odd.

The only even numbers in this sequence are the composite odd powers of 2. [Emmanuel Vantieghem, Jul 08 2013]

If you try to extend this idea to the divisors, the only integer which is satisfied is 1.

Extension to prime power divisors is possible. [Emmanuel Vantieghem, Jul 08 2013]

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006972.

Programs

Mathematica

fQ[n_] := !PrimeQ[n] && Union[ Mod[ n + 1, Transpose[ FactorInteger[n]][[1]] + 1]] == {0}; Select[ Range[20000], fQ[#] &]

PARI

is(n)=my(f=factor(n)[,1]);for(i=1,#f,if((n+1)%(f[i]+1), return(0))); !isprime(n) \\ Charles R Greathouse IV, Jan 15 2015