A268697 Squarefree numbers n such that n^2 + 1 and n^2 - 1 are semiprime.

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

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: A376800 A257832 A050776 * A258358 A090692 A196677

Adjacent sequences: A268694 A268695 A268696 * A268698 A268699 A268700

Keyword

nonn

Author

K. D. Bajpai, Feb 11 2016

Status

approved