A101459 a(k) = card { i*j, i <= k, j <= lcm(1,2,3...,k) }.
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
Offset: 1
Keywords
Examples
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 }
Links
- M. F. Hasler, Table of n, a(n) for n = 1..61
Crossrefs
Cf. A126959.
Programs
-
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);
Comments