cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A071175 Numbers whose product of exponents is equal to the sum of prime factors.

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