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URL: https://oeis.org/A382809

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A382809
a(n) = (6*n + 1)*(12*n + 1)*(18*n + 1).
2
1, 1729, 12025, 38665, 89425, 172081, 294409, 464185, 689185, 977185, 1335961, 1773289, 2296945, 2914705, 3634345, 4463641, 5410369, 6482305, 7687225, 9032905, 10527121, 12177649, 13992265, 15978745, 18144865, 20498401, 23047129, 25798825, 28761265, 31942225, 35349481
OFFSET
0,2
COMMENTS
a(n) is a Carmichael number if all the three factors (6*n + 1), (12*n + 1), and (18*n + 1) are prime (see Chernick and Ribenboim).
REFERENCES
Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 101.
James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 146.
LINKS
Jack Chernick, On Fermat's simple theorem, Bulletin of the American Mathematical Society, Vol. 45, No. 4 (1939), pp. 269-274.
FORMULA
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 3.
G.f.: (1 + 1725*x + 5115*x^2 + 935*x^3)/(1 - x)^4.
E.g.f.: exp(x)*(1 + 1728*x + 4284*x^2 + 1296*x^3).
a(n) = A016921(n) * A017533(n) * A161705(n).
a(n) == 1 (mod 72).
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {1, 1729, 12025, 38665}, 31]
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, Apr 05 2025
STATUS
approved