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 A007438 Moebius transform of triangular numbers. (Formerly M1339) 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 Partial sums of a(n) give A015631(n). - Steve Butler, Apr 18 2006 Equals row sums of triangle A159905. - Gary W. Adamson, Apr 25 2009 REFERENCES 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 = 1..10000 N. J. A. Sloane, Transforms FORMULA 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 MAPLE with(numtheory): a:= proc(n) option remember;        add(mobius(n/d)*d*(d+1)/2, d=divisors(n))     end: seq(a(n), n=1..60);  # Alois P. Heinz, Feb 09 2011 MATHEMATICA a[n_] := Sum[MoebiusMu[n/d]*d*(d+1)/2, {d, Divisors[n]}]; Array[a, 60] (* Jean-François Alcover, Apr 17 2014 *) CROSSREFS Cf. A000217. Cf. A159905. - Gary W. Adamson, Apr 25 2009 Sequence in context: A265793 A126338 A193718 * A230301 A031457 A044990 Adjacent sequences:  A007435 A007436 A007437 * A007439 A007440 A007441 KEYWORD nonn AUTHOR EXTENSIONS Third comment corrected by Mats Granvik, Apr 24 2010 STATUS approved

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Last modified November 22 15:27 EST 2017. Contains 295089 sequences.