A071174 Numbers whose sum of exponents is equal to the product of prime factors.

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, 126877696, 184528125, 307546875, 368947264, 436207616

Offset: 1

Author

Benoit Cloitre, Jun 10 2002

Keywords

• nonn
• easy

Comments

Number k such that A001222(k) = A007947(k). - Amiram Eldar, Jun 24 2022

Examples

			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.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10760 (terms <= 10^52)

Crossrefs

Cf. A001222, A007947, A054411, A054412, A071175.

Programs

Mathematica

q[n_] := Times @@(f = FactorInteger[n])[[;; , 1]] == Total[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),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

Extensions

More terms from Klaus Brockhaus, Jun 12 2002

More terms from Vladeta Jovovic, Jun 13 2002