A290485 The largest 3-Carmichael number that is divisible by the n-th odd prime.

561, 10585, 52633, 561, 530881, 7207201, 1024651, 1615681, 5444489, 471905281, 36765901, 2489462641, 564651361, 958762729, 17316001, 178837201, 1574601601, 7991602081, 597717121, 962442001, 4461725581, 167385219121, 43286923681, 4523928001, 5755495201

Offset: 1

Author

Amiram Eldar, Aug 03 2017

Keywords

• nonn

Comments

Beeger proved in 1950 that if p < q < r are primes such that p*q*r is a Carmichael number, then q < 2p^2 and r < p^3. Therefore there is a finite number of 3-Carmichael numbers which divisible by a given prime.

The terms were calculated using Pinch's tables of Carmichael numbers (see link below).

References

• N. G. W. H. Beeger, "On composite numbers n for which a^n == 1 (mod n) for every a prime to n", Scripta Mathematica, Vol. 16 (1950), pp. 133-135.

Links

• R. G. E. Pinch, Tables relating to Carmichael numbers.

Crossrefs

Cf. A065091 (odd primes), A087788 (3-Carmichael numbers), A141706.