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 A056757 Cube of number of divisors is larger than the number. 20

%I

%S 2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,

%T 34,35,36,38,39,40,42,44,45,46,48,50,51,52,54,55,56,57,58,60,62,63,64,

%U 66,68,70,72,75,76,78,80,81,84,88,90,92,96,98,99,100,102,104,105,108,110

%N Cube of number of divisors is larger than the number.

%C Sequence is finite with 50967 elements. - _Charles R Greathouse IV_, Apr 27, 2011

%C The last odd term is a(15199) = 883575. The odd terms are in A056761. - _T. D. Noe_, May 14 2013

%H Charles R Greathouse IV, <a href="/A056757/b056757.txt">Table of n, a(n) for n = 1..50967</a> (complete sequence)

%F d(n)^3 > n, where d=A000005.

%e n = 27935107200 = 128*27*25*7*11*13*17*19 has 3072 divisors, its cube 28991029248/n = 1.037799, so n is here.

%t t = {}; Do[If[n < DivisorSigma[0,n]^3, AppendTo[t, n]], {n, 10^3}]; t (* _T. D. Noe_, May 14 2013 *)

%t Select[Range[120],DivisorSigma[0,#]^3>#&] (* _Harvey P. Dale_, Apr 22 2019 *)

%o (PARI) is(n)=numdiv(n)^3>n \\ _Charles R Greathouse IV_, Sep 14 2015

%Y Cf. A034884, A035033-A035035.

%Y Cf. A175495 (n < 2^d(n)), A225729-A225738.

%K fini,full,nonn

%O 1,1

%A _Labos Elemer_, Aug 16 2000

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Last modified February 20 11:57 EST 2020. Contains 332076 sequences. (Running on oeis4.)