This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A143822 #13 Sep 22 2022 11:01:02
%S A143822 13,17,23,31,37,53,67,89,97,103,109,113,127,137,149,151,163,167,179,
%T A143822 197,211,223,227,229,241,263,269,277,281,283,311,331,347,359,367,373,
%U A143822 383,389,397,419,431,433,439,479,491,503,509,541,547,587,601,617,619,653
%N A143822 Primes p such that sigma_0((p*p + 1)/2) = 4.
%C A143822 A048161 are primes p such that sigma_0((p*p+1)/2)= 2. Primes p such that sigma_0((p*p+1)/2)= 3 gives all RMS numbers (A140480) with 2 divisors (prime RMS numbers, prime NSW numbers (A088165)) and all RMS numbers with 4 divisors as those are a multiple of two nonequal RMS prime numbers. In general we look after primes p such that sigma_0((p*p+1)/2) equals some given integer k. RMS numbers n=p_1*...*p_t have k=2^t divisors (p_i prime, t integer >=1) and sigma_2(p_1*...*p_t)=(2^t)* (q_1^r_1 *...* q_t^r_t), q_j prime, r_t integer >=1.
%H A143822 Amiram Eldar, <a href="/A143822/b143822.txt">Table of n, a(n) for n = 1..10000</a>
%p A143822 A066885 := proc(n) local p; p :=ithprime(n) ; (p^2+1)/2 ; end: A000005 := proc(n) numtheory[tau](n) ; end: for n from 2 to 300 do if A000005(A066885(n)) = 4 then printf("%d,",ithprime(n)) ; fi; od: # _R. J. Mathar_, Sep 04 2008
%t A143822 Select[Range[650], PrimeQ[#] && DivisorSigma[0, (#^2 + 1)/2] == 4 &] (* _Amiram Eldar_, Mar 11 2020 *)
%t A143822 Select[Prime[Range[150]],DivisorSigma[0,(#^2+1)/2]==4&] (* _Harvey P. Dale_, Sep 22 2022 *)
%Y A143822 Cf. A000005 (sigma_0), A048161, A088165, A140480, A002315.
%K A143822 easy,nonn
%O A143822 1,1
%A A143822 _Ctibor O. Zizka_, Sep 02 2008
%E A143822 97 inserted and extended by _R. J. Mathar_, Sep 04 2008