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A007438
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Moebius transform of triangular numbers.
(Formerly M1339)
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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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 (sbutler(AT)math.ucsd.edu), Apr 18 2006
Partial sums of a(n) give A015631(n) - Steve Butler (sbutler(AT)math.ucsd.edu), Apr 18 2006
Equals row sums of triangle A159905. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 25 2009]
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..10000
N. J. A. Sloane, Transforms
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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
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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
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CROSSREFS
| Cf. A000217.
Cf. A159905. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 25 2009]
Sequence in context: A164570 A126338 A193718 * A031457 A044990 A133146
Adjacent sequences: A007435 A007436 A007437 * A007439 A007440 A007441
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Third comment corrected by Mats Granvik (mats.granvik(AT)abo.fi), Apr 24 2010
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