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A056729 If p | n, then p+1 | n+1 for composite n. 6
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Aug 31 2000
STATUS
approved

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Last modified July 18 13:04 EDT 2024. Contains 374378 sequences. (Running on oeis4.)