cp's OEIS Frontend

A229268 Primes of the form sigma(k) - tau(k), where sigma(k) = A000203(k) and tau(k) = A000005(k).

%I A229268 #24 Jul 28 2025 20:51:17
%S A229268 2,11,353,1013,2333,16369,58579,65519,123733,1982273,7089683,5778653,
%T A229268 12795053,10500593,22586027,19980143,24126653,67108837,72494713,
%U A229268 90781993,106199593,203275951,164118923,183105421,320210549,259997173,794091653,1279963973
%N A229268 Primes of the form sigma(k) - tau(k), where sigma(k) = A000203(k) and tau(k) = A000005(k).
%H A229268 Amiram Eldar, <a href="/A229268/b229268.txt">Table of n, a(n) for n = 1..5000</a>
%F A229268 a(n) = A000203(A065061(n)) - A000005(A065061(n)). - _Michel Marcus_, Sep 21 2013
%F A229268 a(n) = A065608(A065061(n)). - _Amiram Eldar_, Dec 06 2022
%e A229268 Second term of A065061 is 8 and sigma(8) - tau(8) = 15 - 4 = 11 is prime.
%p A229268 with(numtheory); P:=proc(q) local a,n; a:= sigma(n)-tau(n); for n from 1 to q do
%p A229268 if isprime(a) then print(a); fi; od; end: P(10^6);
%t A229268 Join[{2}, Select[(DivisorSigma[1, #] - DivisorSigma[0, #]) & /@ (2*Range[20000]^2), PrimeQ]] (* _Amiram Eldar_, Dec 06 2022 *)
%Y A229268 Cf. A000005, A000010, A000203, A009087, A023194, A038344, A055813, A062700, A064205, A065608, A141242, A229264, A229266
%K A229268 nonn
%O A229268 1,1
%A A229268 _Paolo P. Lava_, Sep 18 2013
%E A229268 More terms from _Michel Marcus_, Sep 21 2013