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A182082 Number of pairs, (x,y), with x >= y, whose LCM does not exceed n. 1
1, 3, 5, 8, 10, 15, 17, 21, 24, 29, 31, 39, 41, 46, 51, 56, 58, 66, 68, 76, 81, 86, 88, 99, 102, 107, 111, 119, 121, 135, 137, 143, 148, 153, 158, 171, 173, 178, 183, 194, 196, 210, 212, 220, 228, 233, 235, 249, 252, 260, 265, 273, 275, 286, 291, 302, 307, 312 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Note that this is the asymmetric count. If all pairs (x,y) are counted, A061503 is obtained. - T. D. Noe, Apr 10 2012

LINKS

Walt Rorie-Baety, Table of n, a(n) for n = 1..1000

Project Euler, Problem 379: Least common multiple count

FORMULA

a(n) = Sum_{k=1..n} (d(k^2)+1)/2, where d is the number of divisors function (A000005). - Charles R Greathouse IV, Apr 10 2012

a(n) = Sum_{k=1..n} A007875(k) * floor(n/k). - Daniel Suteu, Jan 08 2021

EXAMPLE

a(1000000) = 37429395, according to Project Euler problem #379.

MATHEMATICA

Table[Count[Flatten[Table[LCM[i, j], {i, n}, {j, i, n}]], _?(# <= n &)], {n, 60}] (* T. D. Noe, Apr 10 2012 *)

nn = 100; (Accumulate[Table[DivisorSigma[0, n^2], {n, nn}]] + Range[nn])/2 (* T. D. Noe, Apr 10 2012 *)

PROG

(Haskell) a n = length [(x, y)| x <- [1..n], y <- [x..n], lcm x y <= n]

(PARI) a(n)=(sum(k=1, n, numdiv(k^2))+n)/2 \\ Charles R Greathouse IV, Apr 10 2012

CROSSREFS

Cf. A018892, A061503 (symmetric case).

Sequence in context: A024679 A187973 A190488 * A117467 A310025 A133097

Adjacent sequences:  A182079 A182080 A182081 * A182083 A182084 A182085

KEYWORD

nonn

AUTHOR

Walt Rorie-Baety, Apr 10 2012

STATUS

approved

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Last modified April 10 16:05 EDT 2021. Contains 342845 sequences. (Running on oeis4.)