cp's OEIS Frontend

A345335 Primes p such that A014499(k) / A000120(k) is an integer, where k = A000720(p).

%I A345335 #31 Apr 22 2025 02:48:23
%S A345335 2,3,5,7,19,23,29,41,53,67,71,73,83,89,97,113,131,139,193,197,211,269,
%T A345335 281,283,311,317,337,347,349,353,359,373,389,479,503,521,523,547,563,
%U A345335 587,593,601,647,661,691,719,739,839,857,863,881,887,929,937,983,1013
%N A345335 Primes p such that A014499(k) / A000120(k) is an integer, where k = A000720(p).
%C A345335 A014499(k) / A000120(k) = 1 gives A072439.
%H A345335 Robert Israel, <a href="/A345335/b345335.txt">Table of n, a(n) for n = 1..10000</a>
%e A345335 prime(8) = 19, A014499(8)/A000120(8) = 3, thus 19 is a term.
%p A345335 R:= NULL: p:= 1: count:= 0:
%p A345335 for n from 1 while count < 100 do
%p A345335   p:= nextprime(p);
%p A345335   if convert(convert(p,base,2),`+`) mod convert(convert(n,base,2),`+`) = 0 then R:= R,p; count:= count+1 fi;
%p A345335 od:
%p A345335 R; # _Robert Israel_, Apr 21 2025
%t A345335 Select[Range[1000], PrimeQ[#] && Divisible @@ DigitCount[{#, PrimePi[#]}, 2, 1] &] (* _Amiram Eldar_, Jun 14 2021 *)
%o A345335 (PARI) isok(p) = isprime(p) && ((hammingweight(p) % hammingweight(primepi(p))) == 0); \\ _Michel Marcus_, Jun 14 2021
%Y A345335 Cf. A000120, A000720, A014499, A071600, A072439.
%K A345335 nonn,base
%O A345335 1,1
%A A345335 _Ctibor O. Zizka_, Jun 14 2021