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# Talk:Carmichael numbers

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## 1729

*By the way, the Hardy-Ramanujan number, e.g. , is a Carmichael number!*

- 1729 is the Hardy-Ramanujan number ( is smallest integer which is the sum of 2 cubes in 2 ways;)

- 1729 is the third Carmichael number (Cf. A002997;)

- 1729 is the third Zeisel number (Cf. A051015;)

- 1729 is the smallest Chernick's Carmichael number (Cf. A033502.) Product of 3 prime factors (6n+1)(12n+1)(18n+1) with n=1, (Cf. http://www.cs.uwaterloo.ca/journals/JIS/VOL5/Dubner/dubner6.pdf ;)

- 1729 is the smallest abolute Euler pseudoprime. (Cf. A033181;)

- 1729 is the product of 19 * 91 (since 7*13 = 91;)

- 1729 is some figurate number (e.g. the 19
^{th}dodecagonal number, A051624.)

— Karsten Meyer 12:14, 14 November 2010 (UTC)
— Edited by Daniel Forgues 22:13, 14 November 2010 (UTC)

## Tables of Carmichael numbers

— Karsten Meyer 00:40, 15 November 2010 (UTC)

## Chernick's Carmichael numbers

Ther exist some Carmichael numbers, which comply the form (6n+1)*(12n+1)*(18n+1), but one of the "factors" is not prime:

- 172081 = 31 * 61 * 91 5 M3(5)
- 1773289 = 67 * 133 * 199 11 M3(11)
- 4463641 = 91 * 181 * 271 15 M3(15)
- 1110400109 = 557 * 1153 * 1729 96 M3(96)
- 134642101321 = 2821 * 5641 * 8461 470 M3(470)

91 and 133 are Fermat pseudoprimes, and 1729 and 2821 are Carmichael numbers. Nevertheless the numbers fit in the form of Chernick's Carmichael numbers. — Karsten Meyer 01:52, 1 January 2011 (UTC)