Search: id:A115961
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%I A115961
%S A115961 2,6,42,930,44310,5338410,902311410,260630159790,94084209188970,
%T A115961 49770436899273090,41856930884959119930,40224510201386387907030,
%U A115961 55067354465876062759959510,92568222856398333359120816010
%N A115961 a(n)=least number having exactly n distinct prime factors, the largest 
               of which is greater than or equal to sqrt(a(n)).
%F A115961 a(n)=y*(smallest prime that is larger than y), where y is the product 
               of first n-1 consecutive primes.
%F A115961 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 (jvospost3(AT)gmail.com), Feb 13 2006
%e A115961 a(3)=42; indeed, 42=2*3*7, 7>sqrt(42) and 2*3*5 does not qualify because
%e A115961 5<sqrt(30).
%p A115961 a:=n->product(ithprime(j),j=1..n-1)*nextprime(product(ithprime(j),j=1..n-1)): 
               seq(a(n),n=1..16);
%Y A115961 Cf. A115956, A115957, A115958, A115959, A115960.
%Y A115961 Cf. A002110.
%Y A115961 Sequence in context: A116896 A061062 A152479 this_sequence A123137 A014117 
               A054377
%Y A115961 Adjacent sequences: A115958 A115959 A115960 this_sequence A115962 A115963 
               A115964
%K A115961 nonn
%O A115961 1,1
%A A115961 Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 02 2006

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