A174616 Number of eight-prime Carmichael numbers less than 10^n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 89, 655, 3622, 16348, 63635, 223997, 720406, 2148017, 6015901, 16005646, 40696220, 99469866

Offset

0,13

References

Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag, NY, 2004. See p. 220.

Links

Table of n, a(n) for n=0..24.

Claude Goutier, Text file readme.text summarizing enumeration of Carmichael numbers up to 10^22.

Claude Goutier, Text file readme.text summarizing enumeration of Carmichael numbers up to 10^22. [Local copy, with permission]

R. G. E. Pinch, The Carmichael numbers up to 10^21, Proceedings of Conference on Algorithmic Number Theory 2007.

Andrew Shallue and Jonathan Webster, Algorithms for Carmichael numbers, arXiv:2506.09903 [math.NT], 2025-2026.

Index entries for sequences related to Carmichael numbers.

Example

The smallest Carmichael number with 8 prime factors is 232250619601 = 7*11*13*17*31*37*73*163, and there are 6 others, so a(12) = 7.

Crossrefs

For k-prime Carmichael numbers up to 10^n for k = 3,4,...,11, see A132195, A174612, A174613, A174614, A174615, A174616, A174617, A299710, A299711.

Cf. A002997, A006931, A055553.

Sequence in context: A036902 A142204 A071363 * A089394 A068692 A178006

Adjacent sequences: A174613 A174614 A174615 * A174617 A174618 A174619

Keyword

nonn,more

Author

Michel Lagneau, Mar 23 2010

Extensions

a(22) from Claude Goutier added by Amiram Eldar, Apr 19 2024

a(23)-a(24) from Shallue and Webster (2025-2026) added by Amiram Eldar, Jan 24 2026

Status

approved