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A277389 Numbers n such that lambda(n)^3 divides (n-1)^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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Carmichael numbers are composite numbers n such that n = 1 (mod lambda(n)); equivalently, lambda(n)^2 divides (n-1)^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) = p-1 and (p-1)^3 > (p-1)^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) = ((n-1)^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

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)