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Search: id:A115961
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| A115961 |
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a(n)=least number having exactly n distinct prime factors, the largest of which is greater than or equal to sqrt(a(n)). |
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+0
6
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| 2, 6, 42, 930, 44310, 5338410, 902311410, 260630159790, 94084209188970, 49770436899273090, 41856930884959119930, 40224510201386387907030, 55067354465876062759959510, 92568222856398333359120816010
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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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 (jvospost3(AT)gmail.com), Feb 13 2006
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EXAMPLE
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a(3)=42; indeed, 42=2*3*7, 7>sqrt(42) and 2*3*5 does not qualify because
5<sqrt(30).
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MAPLE
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a:=n->product(ithprime(j), j=1..n-1)*nextprime(product(ithprime(j), j=1..n-1)): seq(a(n), n=1..16);
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CROSSREFS
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Cf. A115956, A115957, A115958, A115959, A115960.
Cf. A002110.
Sequence in context: A066864 A116896 A061062 this_sequence A123137 A014117 A054377
Adjacent sequences: A115958 A115959 A115960 this_sequence A115962 A115963 A115964
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 02 2006
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