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A056760 Integers with exactly 2 prime divisors such that the cube of the number of divisors exceeds the number. 2

%I

%S 6,10,12,14,15,18,20,21,22,24,26,28,33,34,35,36,38,39,40,44,45,46,48,

%T 50,51,52,54,55,56,57,58,62,63,68,72,75,76,80,88,92,96,98,99,100,104,

%U 108,112,116,117,124,135,136,144,147,148,152,153,160,162,164,171,172

%N Integers with exactly 2 prime divisors such that the cube of the number of divisors exceeds the number.

%C Numbers with 8 prime divisors also occur among cases satisfying relation d^3>n.

%C Prime divisors are counted without multiplicity. [From Harvey P. Dale, May 14 2012]

%H Donovan Johnson, <a href="/A056760/b056760.txt">Table of n, a(n) for n = 1..254</a> (complete sequence)

%F d[n]^3 > n, n=(p^w)*(q^u), d[]=A000005()

%e The sequence is finite and almost surely complete. Between 270000 and 17000000 no more cases were found. The last 3 entries are: 165888,186624,248832. E.g. n=1024*343=248832, with 66 divisors and d^3=287496>248832

%t Select[Range[180],PrimeNu[#]==2&&DivisorSigma[0,#]^3>#&] (* _Harvey P. Dale_, May 14 2012 *)

%Y A000005, A033033-A033035, A034884.

%K fini,full,nonn

%O 1,1

%A _Labos Elemer_, Aug 16 2000

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Last modified January 16 03:51 EST 2019. Contains 319184 sequences. (Running on oeis4.)