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A265628 Carmichael numbers (A002997) of the form k^3 + 1. 3
1729, 46657, 2628073, 19683001, 110592000001, 432081216001, 2116874304001, 3176523000001, 312328165704192001, 12062716067698821000001, 211215936967181638848001, 411354705193473163968001, 14295706553536348081491001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For the first nine Carmichael numbers of the form k^3 + 1, the values of k + 1 are 13, 37, 139, 271, 4801, 7561, 12841, 14701, 678481 and only 14701 is not a prime number.

The sequence also includes: 32490089562753934948660824001, 782293837499544845175052968001, 611009032634107957276386802479001. - Daniel Suteu, Dec 25 2020

LINKS

Table of n, a(n) for n=1..13.

G. Tarry, I. Franel, A. Korselt, and G. Vacca. Problème chinois, L'intermédiaire des mathématiciens 6 (1899), pp. 142-144.

Eric Weisstein's World of Mathematics, Carmichael Number

Index entries for sequences related to Carmichael numbers

EXAMPLE

2628073 is a term because it is a Carmichael number and 2628073 = 138^3 + 1.

PROG

(PARI) is_c(n) = { my(f); bittest(n, 0) && !for(i=1, #f=factor(n)~, (f[2, i]==1 && n%(f[1, i]-1)==1)||return) && #f>1 }

for(n=1, 1e10, if(is_c(k=n^3+1), print1(k, ", ")))

CROSSREFS

Cf. A002997, A265285, A265328.

Sequence in context: A272935 A284671 A265328 * A306479 A272798 A212920

Adjacent sequences:  A265625 A265626 A265627 * A265629 A265630 A265631

KEYWORD

nonn,hard,more

AUTHOR

Altug Alkan, Dec 10 2015

EXTENSIONS

More terms from Alois P. Heinz, Dec 10 2015

a(10)-a(13) from Daniel Suteu, Dec 25 2020

STATUS

approved

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Last modified January 25 11:49 EST 2022. Contains 350567 sequences. (Running on oeis4.)