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

1,1

Links

Table of n, a(n) for n=1..14.

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

Example

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

Maple

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

Crossrefs

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

Cf. A002110.

Sequence in context: A276453 A152479 A250309 * A355042 A367132 A123137

Adjacent sequences: A115958 A115959 A115960 * A115962 A115963 A115964

Keyword

nonn

Author

Emeric Deutsch, Feb 02 2006

Status

approved