A346068 - OEIS

%I #34 Jul 31 2021 05:15:23

%S 1,9,25,27,121,125,225,243,289,675,961,1089,1125,1331,1681,2187,2601,

%T 3025,3125,3267,3375,3481,4489,4913,6075,6889,7225,7803,8649,11881,

%U 11979,15125,15129,16129,24025,24649,25947,27225,28125,29403,29791,30375,31329,32041,33275,34969

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

%H Amiram Eldar, <a href="/A346068/b346068.txt">Table of n, a(n) for n = 1..10000</a>

%F 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 675 = 3^3 * 5^2 = prime(prime(1))^prime(2) * prime(prime(2))^prime(1), therefore 675 is a term.

%t Join[{1}, Select[Range[35000], AllTrue[Join[PrimePi[(t = Transpose @ FactorInteger[#])[[1]]], t[[2]]], PrimeQ] &]] (* _Amiram Eldar_, Jul 30 2021 *)

%o (Python)

%o from sympy import factorint, isprime, primepi

%o def ok(n):

%o     f = factorint(n)

%o     if not all(isprime(e) for e in f.values()): return False

%o     return all(isprime(primepi(p)) for p in f)

%o print(list(filter(ok, range(35000)))) # _Michael S. Branicky_, Jul 30 2021

%Y Intersection of A056166 and A076610.

%Y Cf. A006450, A302590, A302596, A321874.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Jul 30 2021