

A277389


Numbers n such that lambda(n)^3 divides (n1)^2, where lambda(n) = A002322(n).


2



1, 2, 1729, 19683001, 367804801, 631071001, 2064236401, 2320690177, 24899816449, 40017045601, 110592000001, 137299665601, 432081216001, 479534887801, 760355883001, 1111195454401, 3176523000001, 3495866888449, 3837165696001, 8571867768001, 14373832968001
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OFFSET

1,2


COMMENTS

Carmichael numbers are composite numbers n such that n = 1 (mod lambda(n)); equivalently, lambda(n)^2 divides (n1)^2. As a result, all composite terms of the sequence are Carmichael numbers A002997. But there are no primes in this sequence except for 2 (since lambda(p) = p1 and (p1)^3 > (p1)^2 for p > 2) and so all terms in this sequence other than 1 and 2 are Carmichael numbers.  Charles R Greathouse IV, Oct 15 2016
Is this sequence infinite?


LINKS

Robert Israel and Charles R Greathouse IV, Table of n, a(n) for n = 1..101 (first 58 terms from Robert Israel)


FORMULA

Cf. A002322, A002997, A265628.


PROG

(PARI) isok(n) = ((n1)^2 % (lcm(znstar(n)[2])^3)) == 0; \\ Michel Marcus, Oct 12 2016


CROSSREFS

Sequence in context: A160224 A129061 A233132 * A011541 A080642 A108331
Adjacent sequences: A277386 A277387 A277388 * A277390 A277391 A277392


KEYWORD

nonn


AUTHOR

Thomas Ordowski, Oct 12 2016


EXTENSIONS

a(4) from Michel Marcus, Oct 12 2016
a(5)a(6) from Michel Marcus, Oct 13 2016
More terms from Robert Israel, Oct 13 2016


STATUS

approved



