

A080569


a(n) is the first number in the first run of at least n successive numbers, all having exactly 3 distinct prime factors.


3



30, 230, 644, 1308, 2664, 6850, 10280, 39693, 44360, 48919, 218972, 526095, 526095, 526095, 17233173, 127890362, 29138958036, 146216247221
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OFFSET

1,1


COMMENTS

The 19th term, if it exists, is at least 1.1 * 10^12.  Fred Schneider, Jan 05 2008
There can be at most 209 terms in this sequence. Any list of 210 consecutive numbers must contain a number n which is multiple of 2*3*5*7 = 210. So omega(n) would be >3.  Fred Schneider, Jan 05 2008
Eggleton and MacDougall show that there are no more than 59 terms in this sequence. [From T. D. Noe, Oct 13 2008]
a(19) > 10^13.  Donovan Johnson, Jun 11 2013
a(19) <= 7523987244435061.  Donovan Johnson, Jul 08 2013


LINKS

Table of n, a(n) for n=1..18.
Roger B. Eggleton and James A. MacDougall, Consecutive integers with equally many principal divisors, Math. Mag. 81 (2008), 235248.
Carlos Rivera, Prime Puzzle 427


EXAMPLE

a(3) = 644 because 644 = 2^2 * 7 * 23, so omega(644) = 3, 645 = 3*5*43, so omega(645) = 3 and 646 = 2*17*19, so omega(646) = 3 and no other number n < 644 has omega(n)=omega(n+1)=omega(n+2)=3.


MATHEMATICA

k = 1; Do[ While[ Union[ Table[ Length[ FactorInteger[i]], {i, k, k + n  1}]] != {3}, k++ ]; Print[k], {n, 1, 16}]


PROG

(PARI) k=1; for(i=1, 600000, s=1; for(j=1, k, if(omega(i+j1)!=3, s=0, )); if(s==1, print1(i, ", "); k++; i, ) )


CROSSREFS

Cf. A064708, A064709, A185032, A048932.
Sequence in context: A210101 A156372 A064241 * A185032 A291466 A246892
Adjacent sequences: A080566 A080567 A080568 * A080570 A080571 A080572


KEYWORD

fini,nonn


AUTHOR

Randy L. Ekl, Feb 21 2003


EXTENSIONS

Edited and extended by Robert G. Wilson v, Feb 22 2003
More terms from Don Reble, Mar 02 2003


STATUS

approved



