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

6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 33, 34, 35, 36, 38, 39, 40, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 62, 63, 68, 72, 75, 76, 80, 88, 92, 96, 98, 99, 100, 104, 108, 112, 116, 117, 124, 135, 136, 144, 147, 148, 152, 153, 160, 162, 164, 171, 172

Offset: 1

Author

Labos Elemer, Aug 16 2000

Keywords

• fini
• full
• nonn
• changed

Comments

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

Prime divisors are counted without multiplicity. - Harvey P. Dale, May 14 2012

Examples

			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. k = 1024*343 = 248832, with 66 divisors and d^3 = 287496 > 248832.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..254 (complete sequence)

Crossrefs

Cf. A000005, A033033-A033035, A034884.

Programs

Mathematica

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

Formula

Integers k = (p^w)*(q^u) such that d(k)^3 > k, where d(k) = A000005(k).