cp's OEIS Frontend

A346068 Numbers that are the product of distinct primes with prime subscripts raised to prime powers.

%I A346068 #34 Jul 31 2021 05:15:23
%S A346068 1,9,25,27,121,125,225,243,289,675,961,1089,1125,1331,1681,2187,2601,
%T A346068 3025,3125,3267,3375,3481,4489,4913,6075,6889,7225,7803,8649,11881,
%U A346068 11979,15125,15129,16129,24025,24649,25947,27225,28125,29403,29791,30375,31329,32041,33275,34969
%N A346068 Numbers that are the product of distinct primes with prime subscripts raised to prime powers.
%H A346068 Amiram Eldar, <a href="/A346068/b346068.txt">Table of n, a(n) for n = 1..10000</a>
%F A346068 Sum_{n>=1} 1/a(n) = Product_{p in A006450} (1 + Sum_{q prime} 1/p^q) = 1.2271874... - _Amiram Eldar_, Jul 31 2021
%e A346068 675 = 3^3 * 5^2 = prime(prime(1))^prime(2) * prime(prime(2))^prime(1), therefore 675 is a term.
%t A346068 Join[{1}, Select[Range[35000], AllTrue[Join[PrimePi[(t = Transpose @ FactorInteger[#])[[1]]], t[[2]]], PrimeQ] &]] (* _Amiram Eldar_, Jul 30 2021 *)
%o A346068 (Python)
%o A346068 from sympy import factorint, isprime, primepi
%o A346068 def ok(n):
%o A346068     f = factorint(n)
%o A346068     if not all(isprime(e) for e in f.values()): return False
%o A346068     return all(isprime(primepi(p)) for p in f)
%o A346068 print(list(filter(ok, range(35000)))) # _Michael S. Branicky_, Jul 30 2021
%Y A346068 Intersection of A056166 and A076610.
%Y A346068 Cf. A006450, A302590, A302596, A321874.
%K A346068 nonn
%O A346068 1,2
%A A346068 _Ilya Gutkovskiy_, Jul 30 2021