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A007437
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Inverse Moebius transform of triangular numbers.
(Formerly M3309)
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11
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1, 4, 7, 14, 16, 31, 29, 50, 52, 74, 67, 119, 92, 137, 142, 186, 154, 247, 191, 294, 266, 323, 277, 455, 341, 446, 430, 553, 436, 686, 497, 714, 634, 752, 674, 1001, 704, 935, 878, 1150, 862, 1298, 947, 1323, 1222, 1361, 1129, 1767, 1254, 1674, 1486, 1834
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OFFSET
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1,2
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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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Alois P. Heinz, Table of n, a(n) for n = 1..10000
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210.
N. J. A. Sloane, Transforms
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FORMULA
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Coefficients in expansion of Sum_{n >= 1} x^n/(1-x^n)^3.
G.f.: sum(n>=1, (n*(n+1)/2) * x^n/(1-x^n) ). - Joerg Arndt, Jan 30 2011
a(n)=sum(d|n, d*(d+1)/2)= (1/2) *(sigma(n)+sigma_2(n))= (1/2) *(A000203(n)+A001157(n)). - Benoit Cloitre, Apr 08 2002
Row sums of triangles A134544 and A134545. - Gary W. Adamson, Oct 31 2007
Row sums of triangle A134839 - Gary W. Adamson, Nov 12 2007
Dirichlet g.f. zeta(s)*(zeta(s-1)+zeta(s-2))/2. [From Franklin T. Adams-Watters, Nov 05 2009]
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MAPLE
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with (numtheory):
a:= proc(n) option remember;
add( d*(d+1)/2 , d=divisors(n))
end:
seq (a(n), n=1..60); # Alois P. Heinz, Feb 09 2011
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PROG
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(PARI) a(n)=if(n<1, 1, sumdiv(n, d, (d^2+d))/2); /* Joerg Arndt, Aug 14 2012 */
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CROSSREFS
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Cf. A134544, A134545.
Cf. A134839.
Sequence in context: A055675 A062380 A072031 * A159912 A183060 A209978
Adjacent sequences: A007434 A007435 A007436 * A007438 A007439 A007440
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Christian G. Bower.
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STATUS
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approved
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