A115961 a(n)=least number having exactly n distinct prime factors, the largest of which is greater than or equal to sqrt(a(n)).

2, 6, 42, 930, 44310, 5338410, 902311410, 260630159790, 94084209188970, 49770436899273090, 41856930884959119930, 40224510201386387907030, 55067354465876062759959510, 92568222856398333359120816010

Offset: 1

Author

Emeric Deutsch, Feb 02 2006

Keywords

• nonn

Examples

			a(3)=42; indeed, 42=2*3*7, 7>sqrt(42) and 2*3*5 does not qualify because
5<sqrt(30).
		

Crossrefs

Cf. A115956, A115957, A115958, A115959, A115960.

Cf. A002110.

Programs

Maple

a:=n->product(ithprime(j),j=1..n-1)*nextprime(product(ithprime(j),j=1..n-1)): seq(a(n),n=1..16);

Formula

a(n)=y*(smallest prime that is larger than y), where y is the product of first n-1 consecutive primes.

a(n) = (n-1)# * NextPrime((n-1)#). a(n) = A002110(n-1) * NextPrime(A002110(n-1)). E.g. a(15) = 14# * 13082761331670077 = (2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 * 29 * 31 * 37 * 41 * 43) + 13082761331670077, since 13082761331670077 = 14# + 47 is the least prime > 14#. - Jonathan Vos Post, Feb 13 2006