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A056793
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Number of divisors of lcm(1,...,n).
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1
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1, 2, 4, 6, 12, 12, 24, 32, 48, 48, 96, 96, 192, 192, 192, 240, 480, 480, 960, 960, 960, 960, 1920, 1920, 2880, 2880, 3840, 3840, 7680, 7680, 15360, 18432, 18432, 18432, 18432, 18432, 36864, 36864, 36864, 36864, 73728, 73728, 147456, 147456, 147456, 147456
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 1..1000
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FORMULA
| a(n) = d(lcm(1, .., n)) = A000005(A003418(n));
a(n) = product(floor(log(n)/log(p))+1) where p runs through all prime numbers less than or equal to n. - Wei Zhou, Jun 25 2011
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EXAMPLE
| n = 20: lcm(1,..,20) = 2*2*2*2*3*3*5*7*11*13*17*19 = 232792560 and d(232792560) = 5*3*64 = 960.
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MAPLE
| seq(numtheory[tau](lcm($1..n)), n=1..45); # Nathaniel Johnston, Jun 26 2011
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MATHEMATICA
| Table[DivisorSigma[0, LCM @@ Range[n]], {n, 50}]
Table[Product[Floor[Log[Prime[i], n]] + 1, {i, PrimePi[n]}], {n, 100}] (* Wei Zhou, Jun 25 2011 *)
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CROSSREFS
| Cf. A000005, A003418.
Sequence in context: A062857 A061799 A076868 * A137387 A137394 A062856
Adjacent sequences: A056790 A056791 A056792 * A056794 A056795 A056796
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Aug 28 2000
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