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A007438
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Moebius transform of triangular numbers.
(Formerly M1339)
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12
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1, 2, 5, 7, 14, 13, 27, 26, 39, 38, 65, 50, 90, 75, 100, 100, 152, 111, 189, 148, 198, 185, 275, 196, 310, 258, 333, 294, 434, 292, 495, 392, 490, 440, 588, 438, 702, 549, 684, 584, 860, 582, 945, 730, 876, 803, 1127, 776, 1197, 910, 1168, 1020, 1430
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OFFSET
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1,2
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COMMENTS
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a(n)=|{(x,y):1<=x<=y<=n, gcd(x,y,n)=1}|. E.g. a(4)=7 because of the pairs (1,1), (1,2), (1,3), (1,4), (2,3), (3,3), (3,4). - Steve Butler, Apr 18 2006
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = (A007434(n)+A000010(n))/2, half the sum of the Mobius transforms of n^2 and n. Dirichlet g.f. (zeta(s-2)+zeta(s-1))/(2*zeta(s)). - R. J. Mathar, Feb 09 2011
G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n) = x/(1 - x)^3. - Ilya Gutkovskiy, Apr 25 2017
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MAPLE
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with(numtheory):
a:= proc(n) option remember;
add(mobius(n/d)*d*(d+1)/2, d=divisors(n))
end:
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MATHEMATICA
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a[n_] := Sum[MoebiusMu[n/d]*d*(d+1)/2, {d, Divisors[n]}]; Array[a, 60] (* Jean-François Alcover, Apr 17 2014 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, moebius(n/d)*d*(d+1)/2); \\ Michel Marcus, Nov 05 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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