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A071174
Numbers whose sum of exponents is equal to the product of prime factors.
7
4, 27, 96, 144, 216, 324, 486, 2560, 3125, 6400, 16000, 40000, 57344, 100000, 200704, 250000, 625000, 702464, 823543, 1562500, 2458624, 3906250, 8605184, 23068672, 23914845, 30118144, 39858075, 66430125, 105413504, 110716875
OFFSET
1,1
COMMENTS
Number k such that A001222(k) = A007947(k). - Amiram Eldar, Jun 24 2022
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10760 (terms <= 10^52)
EXAMPLE
57344 = 2^13 * 7^1 and 2*7 = 13+1 hence 57344 is in the sequence.
16000 = 2^7 * 5^3 and 2*5 = 7+3 hence 16000 is in the sequence.
MATHEMATICA
q[n_] := Times @@(f = FactorInteger[n])[[;; , 1]] == Total[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), 1), i))==sum(i=1, o, component(component(factor(n), 2), i)), print1(n, ", ")))
(Python)
from math import prod
from sympy import factorint
def ok(n): f = factorint(n); return sum(f[p] for p in f)==prod(p for p in f)
print(list(filter(ok, range(10**6)))) # Michael S. Branicky, Apr 27 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Benoit Cloitre, Jun 10 2002
EXTENSIONS
More terms from Klaus Brockhaus, Jun 12 2002
More terms from Vladeta Jovovic, Jun 13 2002
STATUS
approved