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A101459
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a(k) = card { i*j, i <= k, j <= lcm(1,2,3...,k) }.
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3
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1, 3, 12, 29, 176, 198, 1608, 3519, 11604, 12500, 152720, 160970, 2292000, 2417700, 2549904, 5336115, 97630080, 101271000, 2055670560, 2125864116, 2209916016, 2291367000, 55764302880, 57138304410, 297081542208
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| See A126959
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LINKS
| M. F. Hasler, Table of n, a(n) for n = 1..61
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EXAMPLE
| a(2) = 3 = #{ i*j, i=1..2, j=1..2 } = #{ 1,2, 2,4 } = #{1,2,4}
a(3) = 12 = #{ 1,2,3,4,5,6, 2,4,6,8,10,12, 3,6,9,12,15,18 } = #{ 1,2,3,4,5,6,8,9,10,12,15,18 }
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MAPLE
| p:=proc(n) option remember; local s, t, i, j: s:=1; t:={}:
for i from n-1 by -1 to 1+n/(min@op@eval@numtheory[factorset])(n) do
t := t union { ilcm(n, i)/n };
t := select( x-> numtheory[divisors](x) intersect t = { x }, t ):
for j in combinat[powerset](t) do s := s+(-1)^nops(j)/ilcm(op(j)) od:
od; s/n end:
a:= k -> ilcm($2..k)*add( p(n), n=1..k);
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CROSSREFS
| Cf. A126959.
Sequence in context: A104353 A001860 A199035 * A051408 A164013 A057671
Adjacent sequences: A101456 A101457 A101458 * A101460 A101461 A101462
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KEYWORD
| nonn
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AUTHOR
| M. F. Hasler (maximilian.hasler(AT)gmail.com), Mar 22 2007
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