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A066843
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Product{k=1 to n} d(k); d(k) is the number of positive divisors of k.
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5
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1, 2, 4, 12, 24, 96, 192, 768, 2304, 9216, 18432, 110592, 221184, 884736, 3538944, 17694720, 35389440, 212336640, 424673280, 2548039680, 10192158720, 40768634880, 81537269760, 652298158080, 1956894474240, 7827577896960
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OFFSET
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1,2
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COMMENTS
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a(n) is also the determinant of the symmetric n X n matrix M defined by M(i,j) = d_3(gcd(i,j)) for 1 <= i,j <= n, where d_3(n) is A007425 - Enrique Pérez Herrero, Aug 12 2011.
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REFERENCES
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Antal Bege, Hadamard product of GCD matrices, Acta Univ. Sapientiae, Mathematica, 1, 1 (2009) 43-49
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,200
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FORMULA
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a(n) = product{p=primes<=n} product{1<=k<=log(n)/log(p)} (1 +1/k)^floor(n/p^k). - Leroy Quet Mar 20 2007
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MAPLE
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with(numtheory):seq(mul(tau(k), k=1..n), n=1..26); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 11 2009]
with(numtheory):a[1]:=1: for n from 2 to 26 do a[n]:=a[n-1]*tau(n) od: seq(a[n], n=1..26); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 21 2009]
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MATHEMATICA
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A066843[n_] := Product[DivisorSigma[0, i], {i, 1, n}]; Array[A066843, 20] (* Enrique Perez Herrero, Aug 12 2011 *)
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PROG
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(PARI) { p=1; for (n=1, 200, p*=length(divisors(n)); write("b066843.txt", n, " ", p) ) } [From Harry J. Smith, Apr 01 2010]
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CROSSREFS
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Cf. A000005
Sequence in context: A129643 A200337 A096421 * A051905 A051426 A048148
Adjacent sequences: A066840 A066841 A066842 * A066844 A066845 A066846
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Jan 20 2002
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STATUS
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approved
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