A055553 Number of Carmichael numbers (A002997) less than 10^n.

0, 0, 1, 7, 16, 43, 105, 255, 646, 1547, 3605, 8241, 19279, 44706, 105212, 246683, 585355, 1401644, 3381806, 8220777, 20138200, 49679870, 123381982, 308279939

Offset

1,4

References

Richard Pinch, Carmichael Numbers up to 10^20, ANTS 7.

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

Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag, NY, 2004. See p. 219.

Links

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

Claude Goutier, Compressed text file carm10e22.7z containing all the Carmichael numbers up to 10^22. [Local copy, with permission. This is a very large file.]

Romeo Meštrović, Generalizations of Carmichael numbers I, arXiv:1305.1867v1 [math.NT], 2013.

Richard G. E. Pinch, The Carmichael numbers up to 10^17, arXiv:math/0504119 [math.NT], 2005.

Richard G. E. Pinch, The Carmichael numbers up to 10^18, arXiv:math/0604376 [math.NT], 2006.

Richard G. E. Pinch, Mathematics research page.

Andrew Shallue and Jonathan Webster, Advances in Tabulating Carmichael Numbers, Research in Number Theory, Vol. 11, No. 8 (2025), pp. 1-8; arXiv preprint, arXiv:2401.14495 [math.NT], 2024.

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

Hermann Stamm-Wilbrandt, Carmichael numbers up to 10^24 converted and stored binary (11.45GB) for PARI/GP fast read, from Jonathan Webster's website.

Eric Weisstein's World of Mathematics, Carmichael Number.

Eric Weisstein's World of Mathematics, Pseudoprime.

Index entries for sequences related to Carmichael numbers.

Prog

(PARI) \\ Uses file from Stamm-Wilbrandt Link above
b=read("carm10e24.bin"); d=10^3; C=0; foreach(b, c, if(c>=d, print1(C", "); d=d*10); C+=1); print(C) \\ Hermann Stamm-Wilbrandt, Mar 07 2026

Crossrefs

Cf. A002997.

Sequence in context: A020941 A318750 A024625 * A066009 A304013 A037241

Adjacent sequences: A055550 A055551 A055552 * A055554 A055555 A055556

Keyword

nonn,more

Author

Eric W. Weisstein

Extensions

Updates from Pinch's articles sent by Charles R Greathouse IV, Dec 04 2005, Jul 16 2006, May 29 2007

a(21) from Pinch's paper by Charles R Greathouse IV, Feb 01 2009

a(22) from Shallue and Webster (2024) added by Amiram Eldar, Feb 23 2024

a(22) = 49679870 reported by Claude Goutier on Dec 28 2022 (see links). - N. J. A. Sloane, Apr 18 2024

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

Status

approved