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

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

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

Sequence in context: A100488 A220019 A225902 * A092364 A296316 A071175

Adjacent sequences: A071171 A071172 A071173 * A071175 A071176 A071177

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