

A056760


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


2



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
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OFFSET

1,1


COMMENTS

Numbers with 8 prime divisors also occur among cases satisfying relation d^3>n.
Prime divisors are counted without multiplicity. [From Harvey P. Dale, May 14 2012]


LINKS

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


FORMULA

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


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. n=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

A000005, A033033A033035, A034884.
Sequence in context: A030231 A267114 A275665 * A084227 A299992 A237051
Adjacent sequences: A056757 A056758 A056759 * A056761 A056762 A056763


KEYWORD

fini,full,nonn


AUTHOR

Labos Elemer, Aug 16 2000


STATUS

approved



