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Brilliant numbers k such that 2k+1 is also brilliant.
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%I #12 Sep 18 2024 14:58:19

%S 4,10,533,671,869,1139,2279,14873,17819,20651,22523,23129,23381,25199,

%T 28013,28943,31439,31571,33899,35369,35621,37241,37403,39059,39449,

%U 41291,42401,42431,42881,43259,45173,45803,49583,49649,49949,50621

%N Brilliant numbers k such that 2k+1 is also brilliant.

%e 1139 is a member because 1139 = 17*67 and 1139*2+1 = 2279 = 43*53.

%o (PARI) isA078972(k)={my(f=factor(k));bigomega(f)==2 && (f[1,2]==2 || logint(f[1,1],10)==logint(f[2,1],10))}

%o isok(k)={isA078972(k) && isA078972(2*k+1)} \\ _Andrew Howroyd_, Sep 18 2024

%Y Subsequence of A111153.

%Y Cf. A078972.

%K base,nonn

%O 1,1

%A _Jason Earls_, _Amarnath Murthy_, Jul 11 2003

%E Offset changed by _Andrew Howroyd_, Sep 18 2024