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A113511
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Product of first A000217(n) = n(n+1)/2 primes.
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1
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1, 2, 30, 30030, 6469693230, 614889782588491410, 40729680599249024150621323470, 2566376117594999414479597815340071648394470, 225319534991831177328890236228992001350685163362356544091910
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) is the smallest squarefree product of a prime, 2-almost prime (semiprime), 3-almost prime, ..., n-almost prime. The analogous sequence without the squarefree 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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LINKS
| Index to divisibility sequences
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FORMULA
| 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
log a(n) ~ n^2 log n. [Charles R Greathouse IV, Jan 13 2012]
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EXAMPLE
| 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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MATHEMATICA
| nn=10; With[{prs=Prime[Range[(nn(nn+1))/2]]}, Table[Times@@Take[prs, (n(n+1))/2], {n, 0, nn}]] (* From Harvey P. Dale, Sep 13 2011 *)
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PROG
| (PARI) a(n)=my(v=primes(n*(n+1)/2)); prod(i=1, #v, v[i]) \\ Charles R Greathouse IV, Jan 13 2012
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CROSSREFS
| Cf. A000217 (triangular numbers), A006125 (2^{n(n-1)/2}).
Cf. A002110, A007467.
Sequence in context: A077521 A203309 A090600 * A062008 A091776 A159578
Adjacent sequences: A113508 A113509 A113510 * A113512 A113513 A113514
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KEYWORD
| nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jan 11 2006
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