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Search: id:A113511
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| 1, 2, 30, 30030, 6469693230, 614889782588491410, 40729680599249024150621323470, 2566376117594999414479597815340071648394470, 225319534991831177328890236228992001350685163362356544091910
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OFFSET
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0,2
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COMMENT
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a(n) is the smallest square-free product of a prime, 2-almost prime (semiprime), 3-almost prime, ..., n-almost prime. The analogous sequence without the square-free condition is A006125(n), n>=2: 2,8,64,1024,32768,....
Cumulative product of A007467. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Mar 17 2007
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FORMULA
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a(n) = prod(k=1, n*(n+1)/2, prime(k)).
a(n) = A002110(A000217(n)). - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Mar 17 2007
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EXAMPLE
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a(4) = 2*(3*5)*(7*11*13)*(17*19*23*29) = 6469693230, the product of the first A000217(4) = 4*5/2 = 10 primes. 6469693230 = 2*15*1001*215441, where 2 is prime, 15 is 2-almost prime, 1001 is 3-almost prime and 215441 is 4-almost prime.
(Of course if the prime factors are rearranged, other primes and almost primes in the same pattern give this same product.)
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CROSSREFS
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Cf. A000217 (triangular numbers), A006125 (2^{n(n-1)/2}).
Cf. A002110, A007467.
Sequence in context: A053851 A077521 A090600 this_sequence A062008 A091776 A069460
Adjacent sequences: A113508 A113509 A113510 this_sequence A113512 A113513 A113514
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KEYWORD
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nonn
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AUTHOR
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Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jan 11 2006
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