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A071175 Numbers whose product of exponents = sum of prime factors. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

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. A054411, A054412.

Sequence in context: A071174 A092364 A296316 * A063262 A156223 A048102

Adjacent sequences:  A071172 A071173 A071174 * A071176 A071177 A071178

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Jun 10 2002

STATUS

approved

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Last modified July 28 15:51 EDT 2021. Contains 346335 sequences. (Running on oeis4.)