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1, 6, 12, 28, 30, 72, 56, 120, 117, 180, 132, 336, 182, 336, 360, 496, 306, 702, 380, 840, 672, 792, 552, 1440, 775, 1092, 1080, 1568, 870, 2160, 992, 2016, 1584, 1836, 1680, 3276, 1406, 2280, 2184, 3600, 1722, 4032, 1892, 3696, 3510, 3312, 2256, 5952
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Dirichlet convolution of sigma_2(n) with phi(n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 27 2002
Equals row sums of triangle A143311 and of triangle A143308. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 06 2008]
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REFERENCES
| B. C. Berndt, Ramanujan's theory of theta-functions, Theta functions: from the classical to the modern, Amer. Math. Soc., Providence, RI, 1993, pp. 1-63. MR 94m:11054. see page 43.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
| Multiplicative with a(p^e) = p^e*(p^(e+1)-1)/(p-1).
G.f.: Sum_{n>0} n^2*x^n/(1-x^n)^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 27 2002
G.f. is phi_2, 1(x) where phi_{r, s}(x)=Sum_{n, m>0} m^r n^s x^{mn}. - Michael Somos, Apr 02 2003
G.f. is also (Q-P^2)/288 where P, Q are Ramanujan sums. - Michael Somos, Apr 02 2003
Dirichlet g.f. zeta(s-1)*zeta(s-2). - R. J. Mathar, Feb 16 2011
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MAPLE
| with(numtheory):seq(sum(sigma(n), k=1..n), n=1..36); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 11 2009]
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MATHEMATICA
| # DivisorSigma[1, #]&/@Range[80] (* From Harvey P. Dale, Mar 12 2011 *)
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PROG
| (PARI) a(n)=if(n<1, 0, n*sigma(n))
(MuPad) numlib::sigma(n)*n$ n=1..81 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 13 2008
(PARI) { for (n=1, 1000, write("b064987.txt", n, " ", n*sigma(n)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 02 2009]
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CROSSREFS
| Cf. A000203, A038040, A002618.
Cf. A000010, A001157.
Cf. A143308, A143311 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 06 2008]
Sequence in context: A009242 A032647 A086792 * A185152 A057341 A068412
Adjacent sequences: A064984 A064985 A064986 * A064988 A064989 A064990
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KEYWORD
| mult,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 30 2001
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