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

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

Author

Benoit Cloitre, Jun 10 2002

Keywords

• easy
• nonn

Comments

Number k such that A005361(k) = A008472(k). - Amiram Eldar, Jun 24 2022

Examples

			55566 = 2^1 * 3^4 * 7^3 and 1*4*3 = 2+3+7 hence 55566 is in the sequence.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005361, A008472, A054411, A054412.

Programs

Mathematica

q[n_] := Total[(f = FactorInteger[n])[[;; , 1]]] == Times @@ f[[;; , 2]]; Select[Range[2, 10^5], q] (* Amiram Eldar, Jun 24 2022 *)

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