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%I #18 Jun 21 2022 08:43:33
%S 8,162,512,32768,41472,3748322,5120000,6837602,8000000,35701250,
%T 75031250,78125000,91125000,907039232,10660336128,11911961250,
%U 21234895362,41265473762,55965865922,209642370242,835707290112,1148179179938,1821331173888,2097152000000
%N Numbers k such that sigma(k) + tau(k) and sigma(k) - tau(k) are primes.
%C Intersection of A064205 and A065061.
%C From _Kevin P. Thompson_, Jun 20 2022: (Start)
%C Terms must be twice a square (see A064205).
%C No terms are congruent to 4 or 6 (mod 10) (see A064205). (End)
%H Donovan Johnson, <a href="/A065116/b065116.txt">Table of n, a(n) for n = 1..250</a>
%e 162 is a term since sigma(162) = 363 and tau(162) = 10 are numbers whose sum (373) and difference (353) are both primes.
%t Do[ds1 = DivisorSigma[1, n]; ds0 = DivisorSigma[0, n]; If[ PrimeQ[ds1 + ds0] && PrimeQ[ds1 - ds0], Print[n]], {n, 1, 10^7} ]
%Y Cf. A064205, A065061.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Nov 12 2001
%E a(10)-a(19) from _Donovan Johnson_, Jul 09 2010
%E a(20)-a(24) from _Donovan Johnson_, Aug 23 2013
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