login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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 A262675 A102834

Adjacent sequences:  A056726 A056727 A056728 * A056730 A056731 A056732

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Aug 31 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 9 04:17 EDT 2021. Contains 343685 sequences. (Running on oeis4.)