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Cube of number of divisors is larger than the number.
21

%I #34 Jun 02 2024 10:17:58

%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 51261 terms. - _Charles R Greathouse IV_, Apr 27 2011 [Corrected by _Amiram Eldar_, Jun 02 2024]

%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..51261</a> (complete sequence, corrected by Amiram Eldar)

%F { k : A000005(k)^3 > k}.

%e k = 27935107200 = 128*27*25*7*11*13*17*19 has 3072 divisors, 3072^3/k = 1.03779..., so k is a term.

%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. A000005, A034884, A035033, A035034, A035035, A056761, A066693.

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

%K fini,full,nonn

%O 1,1

%A _Labos Elemer_, Aug 16 2000