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

1,1

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

Links

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

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A000005, A033033-A033035, A034884.

Sequence in context: A030231 A267114 A275665 * A328956 A084227 A299992

Adjacent sequences: A056757 A056758 A056759 * A056761 A056762 A056763

Keyword

fini,full,nonn

Author

Labos Elemer, Aug 16 2000

Status

approved