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 A088542 #14 Jul 20 2023 12:12:17
%S A088542 2,3,7,71,179,547,983,1283,1289,2909,3709,20269,40829,256579,772573
%N A088542 Prime numbers p such that A022559(p) is a multiple of A000720(p).
%C A088542 Also primes p such that the number of prime factors (with repetition) of p! is a multiple of the number of different prime factors of p! (Prime numbers in A088533).
%e A088542 A022559(7) = 8 is a multiple of A000720(7) = 4.
%t A088542 a = {2}; b = {1}; For[n = 3, n < 1000, n++, If[PrimeQ[n], AppendTo[b, 1], c = FactorInteger[n]; For[j = 1, j < Length[c] + 1, j++, b[[PrimePi[c[[j, 1]]]]] = b[[PrimePi[c[[j, 1]]]]] + c[[j, 2]]]]; If[Mod[Plus @@ b, Length[b]] == 0, If[PrimeQ[n], AppendTo[a, n]]]]; a
%t A088542 Select[Prime[Range[530]],Divisible[PrimeOmega[#!],PrimeNu[#!]]&] (* The program generates the first 11 terms of the sequence. To generate more, increase the Range constant, but the program will then take a long time to run. *) (* _Harvey P. Dale_, Jan 01 2020 *)
%o A088542 (PARI) for(x=2,10000,x1=x!;y=bigomega(x1)/omega(x1); if(y==floor(y),if(isprime(x), print1((x)","))))
%Y A088542 Cf. A000720, A022559, A088533.
%K A088542 nonn,hard,more
%O A088542 1,1
%A A088542 _Cino Hilliard_, Nov 16 2003
%E A088542 Edited and extended by _Stefan Steinerberger_, Dec 11 2007
%E A088542 Offset corrected by _Mohammed Yaseen_, Jul 20 2023
%E A088542 a(14)-a(15) from _Alois P. Heinz_, Jul 20 2023