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%I #22 Jun 24 2022 04:34:15
%S 4,27,96,486,640,1440,2025,2400,2744,3024,3125,3528,3584,4032,4536,
%T 4860,5292,5625,9408,11907,12150,12348,14256,15360,16464,17424,20412,
%U 22400,22464,25344,31360,32805,36504,37500,39204,55566,56250,57624,59904,70304,71442
%N Numbers whose product of exponents is equal to the sum of prime factors.
%C Number k such that A005361(k) = A008472(k). - _Amiram Eldar_, Jun 24 2022
%H Giovanni Resta, <a href="/A071175/b071175.txt">Table of n, a(n) for n = 1..10000</a>
%e 55566 = 2^1 * 3^4 * 7^3 and 1*4*3 = 2+3+7 hence 55566 is in the sequence.
%t q[n_] := Total[(f = FactorInteger[n])[[;; , 1]]] == Times @@ 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),2),i))==sum(i=1,o, component(component(factor(n),1),i)),print1(n,",")))
%o (Python)
%o from math import prod
%o from sympy import factorint
%o def ok(n): f = factorint(n); return prod(f[p] for p in f)==sum(p for p in f)
%o print(list(filter(ok, range(10**5)))) # _Michael S. Branicky_, Apr 27 2021
%Y Cf. A005361, A008472, A054411, A054412.
%K easy,nonn
%O 1,1
%A _Benoit Cloitre_, Jun 10 2002
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