The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A007438 Moebius transform of triangular numbers. (Formerly M1339) 8
 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; corrected by Mats Granvik, Apr 24 2010 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 *) PROG (PARI) a(n) = sumdiv(n, d, moebius(n/d)*d*(d+1)/2); \\ Michel Marcus, Nov 05 2018 CROSSREFS Cf. A000217. Cf. A159905. - Gary W. Adamson, Apr 25 2009 Sequence in context: A126338 A305993 A193718 * A230301 A031457 A044990 Adjacent sequences:  A007435 A007436 A007437 * A007439 A007440 A007441 KEYWORD nonn AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 30 12:10 EDT 2020. Contains 333125 sequences. (Running on oeis4.)