A071174 - OEIS

%I #28 Jun 24 2022 04:34:09

%S 4,27,96,144,216,324,486,2560,3125,6400,16000,40000,57344,100000,

%T 200704,250000,625000,702464,823543,1562500,2458624,3906250,8605184,

%U 23068672,23914845,30118144,39858075,66430125,105413504,110716875

%N Numbers whose sum of exponents is equal to the product of prime factors.

%C Number k such that A001222(k) = A007947(k). - _Amiram Eldar_, Jun 24 2022

%H David A. Corneth, <a href="/A071174/b071174.txt">Table of n, a(n) for n = 1..10760</a> (terms <= 10^52)

%e 57344 = 2^13 * 7^1 and 2*7 = 13+1 hence 57344 is in the sequence.

%e 16000 = 2^7 * 5^3 and 2*5 = 7+3 hence 16000 is in the sequence.

%t q[n_] := Times @@(f = FactorInteger[n])[[;; , 1]] == Total[f[[;; , 2]]]; Select[Range[2, 10^5], q] (* _Amiram Eldar_, Jun 24 2022 *)

%o (PARI) for(n=1,200000,o=omega(n); if(prod(i=1,o, component(component(factor(n),1),i))==sum(i=1,o, component(component(factor(n),2),i)),print1(n,",")))

%o (Python)

%o from math import prod

%o from sympy import factorint

%o def ok(n): f = factorint(n); return sum(f[p] for p in f)==prod(p for p in f)

%o print(list(filter(ok, range(10**6)))) # _Michael S. Branicky_, Apr 27 2021

%Y Cf. A001222, A007947, A054411, A054412, A071175.

%K nonn,easy

%O 1,1

%A _Benoit Cloitre_, Jun 10 2002

%E More terms from _Klaus Brockhaus_, Jun 12 2002

%E More terms from _Vladeta Jovovic_, Jun 13 2002