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A268697 Squarefree numbers n such that n^2 + 1 and n^2 - 1 are semiprime. 2
30, 42, 102, 462, 2130, 2802, 3930, 5658, 6198, 6270, 6870, 7458, 7590, 8970, 9042, 9858, 10302, 11490, 11778, 13710, 13722, 13998, 14322, 17490, 17790, 18042, 19470, 20478, 22278, 22962, 23910, 25998, 29670, 30390, 31722, 32190, 32370, 32610, 32802, 32910, 33330 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All terms are divisible by 6.

Subset of A014574. - Robert Israel, Feb 11 2016

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1) = 30 = 2 * 3 * 5 which is squarefree. 30^2 + 1 = 901 = 17 * 53; 30^2 - 1 = 899 = 29 * 31; 901 and 899 are both semiprime.

a(2) = 42 = 2 * 3 * 7 which is squarefree. 42^2 + 1 = 1765 = 5 * 353; 30^2 - 1 = 1763 = 41 * 43; 1765 and 1763 are both semiprime.

MAPLE

with(numtheory):A268697 := proc(n) if issqrfree(n) and bigomega(n^2+1)=2 and bigomega(n^2-1)=2 then RETURN (n); fi; end: seq(A268697 (n), n=2..10000);

MATHEMATICA

Select[Range[100000], SquareFreeQ[#] && PrimeOmega[#^2 + 1] == 2 && PrimeOmega[#^2 - 1] == 2 &]

PROG

(PARI) for(n=2, 1000, issquarefree(n) & bigomega(n^2 + 1)==2 & bigomega(n^2 - 1)==2 & print1(n, ", "))

(MAGMA) IsP2:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [2..50000] | IsSquarefree(n) and IsP2(n^2+1) and IsP2(n^2-1)];

CROSSREFS

Cf. A001358, A005117, A014574, A039956, A268641.

Sequence in context: A219742 A257832 A050776 * A258358 A090692 A196677

Adjacent sequences:  A268694 A268695 A268696 * A268698 A268699 A268700

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Feb 11 2016

STATUS

approved

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Last modified January 25 05:31 EST 2021. Contains 340416 sequences. (Running on oeis4.)