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Primes of the form sigma(n) - tau(n), where sigma(n) = A000203(n) and tau(n) = A000005(n).
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%I #21 Dec 06 2022 07:56:59

%S 2,11,353,1013,2333,16369,58579,65519,123733,1982273,7089683,5778653,

%T 12795053,10500593,22586027,19980143,24126653,67108837,72494713,

%U 90781993,106199593,203275951,164118923,183105421,320210549,259997173,794091653,1279963973

%N Primes of the form sigma(n) - tau(n), where sigma(n) = A000203(n) and tau(n) = A000005(n).

%H Amiram Eldar, <a href="/A229268/b229268.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) = A000203(A065061(n)) - A000005(A065061(n)). - _Michel Marcus_, Sep 21 2013

%F a(n) = A065608(A065061(n)). - _Amiram Eldar_, Dec 06 2022

%e Second term of A065061 is 8 and sigma(8) - tau(8) = 15 - 4 = 11 is prime.

%p with(numtheory); P:=proc(q) local a,n; a:= sigma(n)-tau(n); for n from 1 to q do

%p if isprime(a) then print(a); fi; od; end: P(10^6);

%t Join[{2}, Select[(DivisorSigma[1, #] - DivisorSigma[0, #]) & /@ (2*Range[20000]^2), PrimeQ]] (* _Amiram Eldar_, Dec 06 2022 *)

%Y Cf. A000005, A000010, A000203, A009087, A023194, A038344, A055813, A062700, A064205, A065608, A141242, A229264, A229266

%K nonn

%O 1,1

%A _Paolo P. Lava_, Sep 18 2013

%E More terms from _Michel Marcus_, Sep 21 2013