A087442 Numbers n such that n is not the power of a prime and such that for every prime divisor p of n, p-1 divides n-1.

45, 225, 325, 405, 561, 637, 891, 1105, 1125, 1225, 1377, 1729, 2025, 2465, 2821, 3321, 3645, 3751, 3825, 4225, 4961, 5589, 5625, 6517, 6525, 6601, 7381, 8125, 8281, 8625, 8911, 9801, 10125, 10585, 10625, 12025, 13357, 13833, 14161, 15841, 15925

Offset: 1

Author

Jens Voß, Sep 04 2003

Keywords

• easy
• nonn

Comments

Weak Carmichael numbers that are not prime powers [Mestrovic] - N. J. A. Sloane, Aug 25 2013

The values of this sequence together with the set of prime powers (A000961) forms the sequence A087441.

Examples

			45 is in A087442 because it is not a prime power and because its prime divisors are 3 and 5 and 3-1=2 as well as 5-1=4 divide 45-1 = 44.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Romeo Meštrović, Generalizations of Carmichael numbers I, arXiv:1305.1867v1 [math.NT], May 4, 2013.

Crossrefs

Cf. A000961, A087441, A225498.

Programs

GAP

for i in [2..20000] do if IsSubset (DivisorsInt(i-1), Set (FactorsInt (i)) - 1) and not IsPrimePowerInt (i) then Print (i, ", "); fi; od;

Mathematica

wcQ[n_] := Length[(p = FactorInteger[n][[;;,1]])] > 1 && AllTrue[p, Divisible[n-1, #-1] &]; Select[Range[10^4], wcQ] (* Amiram Eldar, Sep 22 2019 *)