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

Author

Michel Marcus, Nov 19 2012

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A000203, A007955.

Programs

Mathematica

Select[Range[1000], Times @@ Divisors[#] > Times @@ Divisors[DivisorSigma[1, #]] &] (* T. D. Noe, Nov 19 2012 *)

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