A174615 Number of seven-prime Carmichael numbers less than 10^n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 41, 262, 1340, 5359, 19210, 60150, 172234, 460553, 1159167, 2774702, 6363475, 14056367, 30038569, 62338997

Offset

0,11

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 7 prime factors is 5394826801 = 7*13*17*23*31*67*73, and there is one other 10-digit example, so a(10)=2.

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: A212837 A063271 A142160 * A109125 A037061 A065587

Adjacent sequences: A174612 A174613 A174614 * A174616 A174617 A174618

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