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

1,1

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

Table of n, a(n) for n=1..25.

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

Crossrefs

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

Sequence in context: A290945 A063400 A141706 * A213071 A232761 A232755

Adjacent sequences: A290482 A290483 A290484 * A290486 A290487 A290488

Keyword

nonn

Author

Amiram Eldar, Aug 03 2017

Status

approved