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A101459 a(k) = card { i*j, i <= k, j <= lcm(1,2,3...,k) }.

%I A101459 #28 Jan 06 2015 17:15:37
%S A101459 1,3,12,29,176,198,1608,3519,11604,12500,152720,160970,2292000,
%T A101459 2417700,2549904,5336115,97630080,101271000,2055670560,2125864116,
%U A101459 2209916016,2291367000,55764302880,57138304410,297081542208
%N A101459 a(k) = card { i*j, i <= k, j <= lcm(1,2,3...,k) }.
%C A101459 See A126959.
%H A101459 M. F. Hasler, <a href="/A101459/b101459.txt">Table of n, a(n) for n = 1..61</a>
%e A101459 a(2) = 3 = #{ i*j, i=1..2, j=1..2 } = #{ 1,2, 2,4 } = #{1,2,4}
%e A101459 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 }
%p A101459 p:=proc(n) option remember;local s,t,i,j: s:=1; t:={}:
%p A101459 for i from n-1 by -1 to 1+n/(min@op@eval@numtheory[factorset])(n) do
%p A101459 t := t union { ilcm(n,i)/n };
%p A101459 t := select( x-> numtheory[divisors](x) intersect t = { x }, t ):
%p A101459 for j in combinat[powerset](t) do s := s+(-1)^nops(j)/ilcm(op(j)) od:
%p A101459 od; s/n end:
%p A101459 a:= k -> ilcm($2..k)*add( p(n), n=1..k);
%Y A101459 Cf. A126959.
%K A101459 nonn
%O A101459 1,2
%A A101459 _M. F. Hasler_, Mar 22 2007