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Numbers k such that k < d(k)^(22/10), where d(k) is the number of divisors of k.
3

%I #11 Apr 10 2024 15:06:52

%S 2,3,4,6,8,9,10,12,14,15,16,18,20,21,24,28,30,32,36,40,42,44,45,48,50,

%T 54,56,60,64,66,70,72,78,80,84,88,90,96,100,108,112,120,126,132,140,

%U 144,150,156,160,168,180,192,198,200,204,210,216,220,224,228,234

%N Numbers k such that k < d(k)^(22/10), where d(k) is the number of divisors of k.

%C Alternatively, we could write k^5 < d(k)^11. The last odd number is a(23) = 45.

%H T. D. Noe, <a href="/A225730/b225730.txt">Table of n, a(n) for n = 1..155</a> (complete sequence)

%t t = {}; Do[If[n < DivisorSigma[0, n]^(22/10), AppendTo[t, n]], {n, 10^5}]; t

%t Select[Range[250],#<DivisorSigma[0,#]^(22/10)&] (* _Harvey P. Dale_, Apr 10 2024 *)

%o (PARI) for (k=2, 20000, if (k^5 < numdiv(k)^11, print1(k,", "))) \\ _Hugo Pfoertner_, Apr 25 2023

%Y Cf. A000005, A034884 (k < d(k)^2), A175495 (k < 2^d(k)), A056757 (k < d(k)^3).

%Y Cf. A225729-A225738, A353448.

%K nonn,fini,full

%O 1,1

%A _T. D. Noe_, May 14 2013