OFFSET
2,1
COMMENTS
The first term is the Hardy-Ramanujan number. - Omar E. Pol, Nov 25 2019
LINKS
Amiram Eldar, Table of n, a(n) for n = 2..2905 (calculated using data from Claude Goutier; terms 2..831 from Daniel Suteu)
Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.
Daniel Suteu, Terms and upper bounds for n = 2..10000 (values greater than 2^64 are upper bounds).
Eric Weisstein's World of Mathematics, Carmichael Number.
EXAMPLE
a(2) = 1729 = (2*3 + 1)(2*2*3 + 1)(2*3*3 + 1).
a(3) = 252601 = (2*2*2*5 + 1)(2*2*3*5 + 1)(2*2*5*5 + 1).
a(4) = 1152271 = (2*3*7 + 1)(2*3*3*7 + 1)(2*3*5*7 + 1).
a(5) = 1615681 = (2*11 + 1)(2*3*3*11 + 1)(2*2*2*2*2*11 + 1).
MATHEMATICA
carmQ[n_] := CompositeQ[n] && Divisible[n - 1, CarmichaelLambda[n]]; gpf[n_] := FactorInteger[n][[-1, 1]]; g[n_] := If[Length[(u = Union[gpf /@ (FactorInteger[n][[;; , 1]] - 1)])] == 1, u[[1]], 1]; m = 5; c = 0; k = 0; v = Table[0, {m}]; While[c < m, k++ If[! carmQ[k], Continue[]]; If[(p = g[k]) > 1, i = PrimePi[p] - 1; If[i <= m && v[[i]] == 0, c++; v[[i]] = k]]]; v (* Amiram Eldar, Oct 08 2019 *)
PROG
(Perl) use ntheory ":all"; sub a { my $p = nth_prime(shift); for(my $k = 1; ; ++$k) { return $k if (is_carmichael($k) and vecall { (factor($_-1))[-1] == $p } factor($k)) } }
for my $n (2..10) { print "a($n) = ", a($n), "\n" }
CROSSREFS
KEYWORD
nonn
AUTHOR
Daniel Suteu, Sep 25 2019
STATUS
approved