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

1,1

Comments

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

Links

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

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

Cf. A005361, A008472, A054411, A054412.

Sequence in context: A071174 A092364 A296316 * A352331 A063262 A156223

Adjacent sequences: A071172 A071173 A071174 * A071176 A071177 A071178

Keyword

easy,nonn

Author

Benoit Cloitre, Jun 10 2002

Status

approved