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%I M1339 #44 Nov 05 2018 06:32:23
%S 1,2,5,7,14,13,27,26,39,38,65,50,90,75,100,100,152,111,189,148,198,
%T 185,275,196,310,258,333,294,434,292,495,392,490,440,588,438,702,549,
%U 684,584,860,582,945,730,876,803,1127,776,1197,910,1168,1020,1430
%N Moebius transform of triangular numbers.
%C 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
%C Partial sums of a(n) give A015631(n). - _Steve Butler_, Apr 18 2006
%C Equals row sums of triangle A159905. - _Gary W. Adamson_, Apr 25 2009; corrected by _Mats Granvik_, Apr 24 2010
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Alois P. Heinz, <a href="/A007438/b007438.txt">Table of n, a(n) for n = 1..10000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F 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
%F G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n) = x/(1 - x)^3. - _Ilya Gutkovskiy_, Apr 25 2017
%p with(numtheory):
%p a:= proc(n) option remember;
%p add(mobius(n/d)*d*(d+1)/2, d=divisors(n))
%p end:
%p seq(a(n), n=1..60); # _Alois P. Heinz_, Feb 09 2011
%t a[n_] := Sum[MoebiusMu[n/d]*d*(d+1)/2, {d, Divisors[n]}]; Array[a, 60] (* _Jean-François Alcover_, Apr 17 2014 *)
%o (PARI) a(n) = sumdiv(n, d, moebius(n/d)*d*(d+1)/2); \\ _Michel Marcus_, Nov 05 2018
%Y Cf. A000217.
%Y Cf. A159905. - _Gary W. Adamson_, Apr 25 2009
%K nonn
%O 1,2
%A _N. J. A. Sloane_.
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