A080062 Composite numbers n such that for all primes p dividing n, p-1 divides n-1.

4, 8, 9, 16, 25, 27, 32, 45, 49, 64, 81, 121, 125, 128, 169, 225, 243, 256, 289, 325, 343, 361, 405, 512, 529, 561, 625, 637, 729, 841, 891, 961, 1024, 1105, 1125, 1225, 1331, 1369, 1377, 1681, 1729, 1849, 2025, 2048, 2187, 2197, 2209, 2401, 2465, 2809, 2821

Offset: 1

Author

Robert G. Wilson v, Jan 23 2003

Keywords

• nonn

Comments

The subsequence of squarefree terms gives the Carmichael numbers (A002997); cf. Korselt's criterion. - Joerg Arndt, May 17 2016

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000
• Wikipedia, Korselt's criterion

Crossrefs

Cf. A056729, A079543.

Cf. A002997 (Carmichael numbers).

Programs

Mathematica

Select[ Range[2, 10^4], !PrimeQ[ # ] && Union[ Mod[ # - 1, Transpose[ FactorInteger[ # ]][[1]] - 1]] == {0} &]

PARI

is080062(n)=if(isprime(n),return(0)); my(f=factor(n)[, 1]); for(j=1, #f, if((n-1)%(f[j]-1), return(0))); 1; \\ Joerg Arndt, May 17 2016