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A064708 Initial term of run of (at least) n consecutive numbers with just 2 distinct prime factors. 4
6, 14, 20, 33, 54, 91, 141, 141 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It can be shown by an application of Mihailescu's theorem that a(12) does not exist, since then there would be two 3-smooth numbers close together (it suffices to check up to 2*3^3).

REFERENCES

Roger B. Eggleton and James A. MacDougall, Consecutive integers with equally many principal divisors, Math. Mag 81 (2008), 235-248. [From T. D. Noe, Oct 13 2008]

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

6 = 2*3; 14 = 2*7 and 15 = 3*5; 20 = 2^2*5, 21 = 3*7 and 22 = 2*11; 33 = 3*11, 34 = 2*17, 35 = 5*7 and 36 = (2*3)^2; etc.

CROSSREFS

Cf. A064709.

Sequence in context: A101567 A123267 A236928 * A064709 A118129 A046712

Adjacent sequences:  A064705 A064706 A064707 * A064709 A064710 A064711

KEYWORD

nonn,fini

AUTHOR

Robert G. Wilson v, Oct 13 2001

EXTENSIONS

If a(9) exists, it is greater than 10^30. - Don Reble (djr(AT)nk.ca), Mar 02 2003

If a(9) exists, it is greater than 10^3000. - Charles R Greathouse IV, Apr 22 2009

STATUS

approved

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Last modified June 24 11:40 EDT 2017. Contains 288697 sequences.