A219364 Numbers such that the product of divisors of n is greater than the product of divisors of sigma(n).

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Cf. A000203, A007955.

Sequence in context: A102646 A104021 A073804 * A195212 A332443 A313323

Adjacent sequences: A219361 A219362 A219363 * A219365 A219366 A219367

Keyword

nonn,easy

Author

Michel Marcus, Nov 19 2012

Status

approved