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A292538 Lucas-Carmichael numbers of the form k^2 - 1. 1
399, 2915, 7055, 63503, 147455, 1587599, 1710863, 2249999, 2924099, 6656399, 9486399, 14288399, 19289663, 25603599, 26936099, 28451555, 31270463, 32148899, 45158399, 49280399, 71368703, 91011599, 105884099, 111513599, 144288143, 146894399, 150405695 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection of A005563 and A006972.

The numbers k such that k^2 - 1 is a Lucas-Carmichael number are 20, 54, 84, 252, 384, 1260, 1308, 1500, 1710, 2580, 3080, 3780, 4392, ...

LINKS

Table of n, a(n) for n=1..27.

MAPLE

filter:= t ->

  andmap(f -> f[2]=1 and (t+1) mod (f[1]+1) = 0, ifactors(t)[2]):

select(filter, [seq(k^2-1, k=3..10^5)]); # Robert Israel, Sep 24 2017

MATHEMATICA

lcQ[n_] := !PrimeQ[n] && Union[Transpose[FactorInteger[n]][[2]]] == {1} && Union[Mod[n + 1, Transpose[FactorInteger[n]][[1]] + 1]] == {0}; Select[Range[2, 10^4]^2 - 1, lcQ]

CROSSREFS

Cf. A005563, A006972.

Sequence in context: A292573 A299213 A206536 * A065767 A166915 A110885

Adjacent sequences:  A292535 A292536 A292537 * A292539 A292540 A292541

KEYWORD

nonn

AUTHOR

Amiram Eldar, Sep 18 2017

STATUS

approved

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Last modified May 26 15:29 EDT 2019. Contains 323597 sequences. (Running on oeis4.)