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A324317 Number of primary Carmichael numbers (A324316) less than 10^n. 10
0, 0, 0, 2, 4, 9, 19, 51, 107, 219, 417, 757, 1470, 2666, 5040, 9280, 17210, 32039 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The number of Carmichael numbers (A002997) less than 10^n is 0, 0, 1, 7, 16, 43, 105, 255, 646, 1547, 3605, 8241, 19279, 44706, 105212, 246683, 585355, 1401644, ... (see A055553).

The terms up to a(10) are given in Table 1 of Kellner and Sondow 2019. The terms up to a(18) and related results are given in Table 1.5 of Kellner 2019.

All computations depend on Pinch's database.

LINKS

Table of n, a(n) for n=1..18.

Bernd C. Kellner and Jonathan Sondow, Power-Sum Denominators, Amer. Math. Monthly, 124 (2017), 695-709; arXiv:1705.03857 [math.NT], 2017.

Bernd C. Kellner and Jonathan Sondow, On Carmichael and polygonal numbers, Bernoulli polynomials, and sums of base-p digits, arXiv:1902.10672 [math.NT], 2019.

Bernd C. Kellner, On primary Carmichael numbers, arXiv:1902.11283 [math.NT], 2019.

R. G. E. Pinch, The Carmichael numbers up to 10^18, 2008.

EXAMPLE

There are two primary Carmichael numbers less than 10^4, namely, 1729 and 2821, so a(4) = 2.

CROSSREFS

Cf. A002997, A055553, A324315, A324316, A324318, A324319, A324320, A324369, A324370, A324371, A324404, A324405.

Sequence in context: A153447 A076893 A176501 * A096354 A076838 A034749

Adjacent sequences:  A324314 A324315 A324316 * A324318 A324319 A324320

KEYWORD

nonn,base,more,hard

AUTHOR

Bernd C. Kellner and Jonathan Sondow, Feb 22 2019

EXTENSIONS

a(11)-a(18) from Amiram Eldar, Mar 01 2019

STATUS

approved

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)