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A219364
Numbers such that the product of divisors of n is greater than the product of divisors of sigma(n).
2
4, 9, 16, 18, 25, 36, 48, 50, 64, 72, 80, 81, 100, 112, 144, 162, 192, 200, 208, 225, 240, 256, 288, 289, 300, 320, 324, 336, 400, 432, 441, 448, 450, 468, 484, 512, 576, 578, 592, 624, 625, 648, 676, 704, 720, 729, 768, 784, 800, 832, 882, 900, 960, 976
OFFSET
1,1
COMMENTS
That is, numbers satisfying A007955(n) > A007955(A000203(n)).
LINKS
F. Luca, On the product of divisors of n and sigma(n), J. Inequal. Pure Appl. Math., Volume 4, Issue 2, Article 46, 2003.
MATHEMATICA
Select[Range[1000], Times @@ Divisors[#] > Times @@ Divisors[DivisorSigma[1, #]] &] (* T. D. Noe, Nov 19 2012 *)
PROG
(PARI) A007955(n)=if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2))
is(n)=A007955(n)>A007955(sigma(n)) \\ Charles R Greathouse IV, Feb 04 2013
(Python)
from math import isqrt
from itertools import count, islice
from sympy import divisor_count, divisor_sigma
def A219364_gen(): # generator of terms
return filter(lambda n: (f:=(lambda m:isqrt(m)**c if (c:=divisor_count(m)) & 1 else m**(c//2)))(n) > f(divisor_sigma(n)), count(1))
A219364_list = list(islice(A219364_gen(), 20)) # Chai Wah Wu, Jun 25 2022
CROSSREFS
Sequence in context: A102646 A104021 A073804 * A195212 A332443 A313323
KEYWORD
nonn,easy
AUTHOR
Michel Marcus, Nov 19 2012
STATUS
approved