cp's OEIS Frontend

A385288 Numbers with a prime number of prime factors, counted with multiplicity, and whose prime factors are each raised to a prime exponent.

%I A385288 #22 Jun 25 2025 18:04:07
%S A385288 4,8,9,25,27,32,49,72,108,121,125,128,169,200,243,288,289,343,361,392,
%T A385288 500,529,675,800,841,961,968,972,1125,1323,1331,1352,1369,1372,1568,
%U A385288 1681,1800,1849,2048,2187,2197,2209,2312,2700,2809,2888,3087,3125,3267,3481
%N A385288 Numbers with a prime number of prime factors, counted with multiplicity, and whose prime factors are each raised to a prime exponent.
%C A385288 a(n) = A114129(n) through n=25; then a(26) = 961 and A114129(26) = 864.
%C A385288 Subset of A056166.
%C A385288 Subset of A001694. - _Michael De Vlieger_, Jun 25 2025.
%H A385288 James C. McMahon, <a href="/A385288/b385288.txt">Table of n, a(n) for n = 1..1000</a>
%e A385288 200 = 2^3 * 5^2; 200 has a prime number of prime factors, counted with multiplicity (3 + 2 = 5), and exponents 3 and 2 are prime.
%t A385288 Select[Range[10^4],AllTrue[Last/@FactorInteger[#],PrimeQ]&&PrimeQ[PrimeOmega[#]]&]
%o A385288 (PARI) isok(k) = my(f=factor(k)); isprime(bigomega(k)) && (sum(k=1, #f~, isprime(f[k,2])) == omega(f)); \\ _Michel Marcus_, Jun 25 2025
%Y A385288 Cf. A001248, A001694, A030078, A056166, A114129.
%K A385288 nonn
%O A385288 1,1
%A A385288 _James C. McMahon_, Jun 24 2025