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 A006580 a(n) = Sum_{k=1..n-1} lcm(k,n-k). (Formerly M3336) 5
 0, 0, 1, 4, 8, 20, 21, 56, 60, 96, 105, 220, 152, 364, 301, 360, 464, 816, 549, 1140, 760, 1036, 1221, 2024, 1196, 2200, 2041, 2484, 2184, 4060, 2205, 4960, 3664, 4224, 4641, 5180, 4008, 8436, 6517, 7072, 5980, 11480, 6321, 13244, 8888, 9540, 11661, 17296 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES Marc LeBrun, personal communication. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1000 terms from Reinhard Zumkeller) Marc Le Brun, Email to N. J. A. Sloane, Jul 1991. FORMULA For n > 0, a(n) = (n/6)*Sum_{d|n} (d*phi(d) - A023900(d)). - Sebastian Karlsson, Oct 02 2021 a(n) = (n/6) * (A057660(n) - A130054(n)), for n > 0. - Amiram Eldar, Apr 28 2023 MAPLE a:= n-> add(ilcm(j, n-j), j=0..n): seq(a(n), n=0..70); # Alois P. Heinz, Aug 25 2019 MATHEMATICA Table[ Sum[ LCM[ k, n-k ], {k, 1, n-1} ], {n, 2, 50} ] (* Olivier Gérard, Aug 15 1997 *) f1[p_, e_] := (p^(2*e + 1) + 1)/(p + 1); f2[p_, e_] := 1 - (p - 1)*e; a[n_] := (Times @@ f1 @@@ (fct = FactorInteger[n]) - Times @@ f2 @@@ fct)*n/6; a[0] = 0; Array[a, 100, 0] (* Amiram Eldar, Apr 28 2023 *) PROG (Haskell) a006580 n = a006580_list !! (n-1) a006580_list = map sum a003990_tabl -- Reinhard Zumkeller, Aug 05 2012 (PARI) a(n) = sum(k=1, n-1, lcm(k, n-k)); \\ Michel Marcus, Aug 11 2017 CROSSREFS Antidiagonal sums of array A003990. Cf. A209295. Cf. A000010, A023900, A057660, A130054. Sequence in context: A273143 A273174 A178447 * A061814 A087254 A160726 Adjacent sequences: A006577 A006578 A006579 * A006581 A006582 A006583 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS More terms from Olivier Gérard, Aug 15 1997 STATUS approved

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Last modified February 29 17:04 EST 2024. Contains 370427 sequences. (Running on oeis4.)