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A071174 Numbers whose sum of exponents = product of prime factors. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

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. 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

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Last modified July 25 18:20 EDT 2021. Contains 346291 sequences. (Running on oeis4.)