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
Keywords
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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)];
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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);
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Mathematica
Select[Range[100000], SquareFreeQ[#] && PrimeOmega[#^2 + 1] == 2 && PrimeOmega[#^2 - 1] == 2 &]
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PARI
for(n=2, 1000, issquarefree(n) & bigomega(n^2 + 1)==2 & bigomega(n^2 - 1)==2 & print1(n, ", "))
Comments