cp's OEIS Frontend

A071174 Numbers whose sum of exponents is equal to the product of prime factors.

%I A071174 #32 Apr 26 2025 03:43:41
%S A071174 4,27,96,144,216,324,486,2560,3125,6400,16000,40000,57344,100000,
%T A071174 200704,250000,625000,702464,823543,1562500,2458624,3906250,8605184,
%U A071174 23068672,23914845,30118144,39858075,66430125,105413504,110716875,126877696,184528125,307546875,368947264,436207616
%N A071174 Numbers whose sum of exponents is equal to the product of prime factors.
%C A071174 Number k such that A001222(k) = A007947(k). - _Amiram Eldar_, Jun 24 2022
%H A071174 David A. Corneth, <a href="/A071174/b071174.txt">Table of n, a(n) for n = 1..10760</a> (terms <= 10^52)
%e A071174 57344 = 2^13 * 7^1 and 2*7 = 13+1 hence 57344 is in the sequence.
%e A071174 16000 = 2^7 * 5^3 and 2*5 = 7+3 hence 16000 is in the sequence.
%t A071174 q[n_] := Times @@(f = FactorInteger[n])[[;; , 1]] == Total[f[[;; , 2]]]; Select[Range[2, 10^5], q] (* _Amiram Eldar_, Jun 24 2022 *)
%o A071174 (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 A071174 (Python)
%o A071174 from math import prod
%o A071174 from sympy import factorint
%o A071174 def ok(n): f = factorint(n); return sum(f[p] for p in f)==prod(p for p in f)
%o A071174 print(list(filter(ok, range(10**6)))) # _Michael S. Branicky_, Apr 27 2021
%Y A071174 Cf. A001222, A007947, A054411, A054412, A071175.
%K A071174 nonn,easy
%O A071174 1,1
%A A071174 _Benoit Cloitre_, Jun 10 2002
%E A071174 More terms from _Klaus Brockhaus_, Jun 12 2002
%E A071174 More terms from _Vladeta Jovovic_, Jun 13 2002