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A268043 Numbers k such that k^3 - 1 and k^3 + 1 are semiprime. 5
6, 1092, 1932, 2730, 4158, 6552, 11172, 25998, 30492, 55440, 76650, 79632, 85092, 102102, 150990, 152082, 152418, 166782, 211218, 235662, 236208, 248640, 264600, 298410, 300300, 301182, 317772, 380310, 387198, 441798, 476028, 488418 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Obviously, k+1 and k-1 are always prime numbers.

LINKS

Table of n, a(n) for n=1..32.

EXAMPLE

a(1) = 6 because 6^3-1 = 215 = 5*43 and 6^3+1 = 217 = 7*31, therefore 215, 217 are both semiprimes.

MATHEMATICA

Select[Range[500000], PrimeOmega[#^3 - 1] == PrimeOmega[#^3 + 1] == 2 &]

PROG

(MAGMA) IsSemiprime:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [2..300000] | IsSemiprime(n^3+1) and IsSemiprime(n^3-1) ];

(PARI) isok(n) = (bigomega(n^3-1) == 2) && (bigomega(n^3+1) == 2); \\ Michel Marcus, Jan 26 2016

CROSSREFS

Subsequence of A014574.

Cf. A002384, A014574, A055494, A088707. A096173, A096175, A109373.

Sequence in context: A125536 A003763 A179853 * A190351 A267071 A219165

Adjacent sequences:  A268040 A268041 A268042 * A268044 A268045 A268046

KEYWORD

nonn

AUTHOR

Vincenzo Librandi, Jan 25 2016

STATUS

approved

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Last modified October 13 16:35 EDT 2019. Contains 327967 sequences. (Running on oeis4.)