

A052215


a(n) = smallest number m such that m and m+1 are the product of exactly n distinct primes.


8



2, 14, 230, 7314, 378014, 11243154, 965009045, 65893166030, 5702759516090, 605247139068494, 78971815814237709, 22593106657425552170
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OFFSET

1,1


COMMENTS

Prime factors may not be repeated in m and m+1. The difference between this sequence and A093548 is that in the latter, prime factors may be repeated. So the present sequence imposes more stringent conditions than A093548, hence a(n) >= A093548(n).  N. J. A. Sloane, Nov 21 2015
A115186(n) <= A093548 (n) <= a(n).  Zak Seidov, Jan 16 2015
2^63 < a(12) <= 22593106657425552170. [Donovan Johnson, Oct 23 2008]
a(12) confirmed to be the upper limit of the range above.  Bert Dobbelaere, Jun 27 2019


LINKS

Table of n, a(n) for n=1..12.


EXAMPLE

14 and 15 are both the product of 2 primes.
230 is the 3rd entry because we have (230=2*5*23, 231=3*7*11).


CROSSREFS

Cf. A093548 (another version), A093549, A093550, A115186, A318896.
Sequence in context: A118086 A048163 A093548 * A053846 A053855 A219344
Adjacent sequences: A052212 A052213 A052214 * A052216 A052217 A052218


KEYWORD

hard,nice,nonn


AUTHOR

Erich Friedman, Jan 29 2000


EXTENSIONS

More terms from Naohiro Nomoto, Jul 08 2001
a(7) from Farideh Firoozbakht, Apr 06 2004
a(8)a(10) from Martin Fuller, Jan 17 2006
a(11) from Donovan Johnson, Oct 23 2008
a(12) from Bert Dobbelaere, Jun 27 2019


STATUS

approved



