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A071175
Numbers whose product of exponents is equal to the sum of prime factors.
5
4, 27, 96, 486, 640, 1440, 2025, 2400, 2744, 3024, 3125, 3528, 3584, 4032, 4536, 4860, 5292, 5625, 9408, 11907, 12150, 12348, 14256, 15360, 16464, 17424, 20412, 22400, 22464, 25344, 31360, 32805, 36504, 37500, 39204, 55566, 56250, 57624, 59904, 70304, 71442
OFFSET
1,1
COMMENTS
Number k such that A005361(k) = A008472(k). - Amiram Eldar, Jun 24 2022
LINKS
EXAMPLE
55566 = 2^1 * 3^4 * 7^3 and 1*4*3 = 2+3+7 hence 55566 is in the sequence.
MATHEMATICA
q[n_] := Total[(f = FactorInteger[n])[[;; , 1]]] == Times @@ f[[;; , 2]]; Select[Range[2, 10^5], q] (* Amiram Eldar, Jun 24 2022 *)
PROG
(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, ", ")))
(Python)
from math import prod
from sympy import factorint
def ok(n): f = factorint(n); return prod(f[p] for p in f)==sum(p for p in f)
print(list(filter(ok, range(10**5)))) # Michael S. Branicky, Apr 27 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Jun 10 2002
STATUS
approved