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

1,1

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A006972.

Sequence in context: A115169 A070495 A270421 * A070265 A354179 A262675

Adjacent sequences: A056726 A056727 A056728 * A056730 A056731 A056732

Keyword

nonn

Author

Robert G. Wilson v, Aug 31 2000

Status

approved