login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A064987 a(n) = n*sigma(n). 32
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; text; internal format)
OFFSET

1,2

COMMENTS

Dirichlet convolution of sigma_2(n) with phi(n). - Vladeta Jovovic, Oct 27 2002

Equals row sums of triangle A143311 and of triangle A143308. [Gary W. Adamson, Aug 06 2008]

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.

G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, AMS Chelsea Publishing, Providence, Rhode Island, 2002, pp. 166-167.

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

M. Planat, Twelve-dimensional Pauli group contextuality with eleven rays, arXiv:1201.5455 [quant-ph], 2012.

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, Oct 27 2002

G.f. is phi_{2, 1}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}. - Michael Somos, Apr 02 2003

G.f. is also (Q - P^2) / 288 where P, Q are Ramanujan Lambert series. - Michael Somos, Apr 02 2003. See the Hardy reference, p. 136, eq. (10.5.4) (with a proof). For Q and P, (10.5.6) and (10.5.5), see E_4 A004009 and E_2 A006352, respectively. - Wolfdieter Lang, Jan 30 2017

Convolution of A000118 and A186690. Dirichlet convolution of A000027 and A000290. - Michael Somos, Mar 25 2012

Dirichlet g.f. zeta(s-1)*zeta(s-2). - R. J. Mathar, Feb 16 2011

a(n) = A009194(n)*A009242(n). - Michel Marcus, Oct 23 2013

a(n) (mod 5) = A126832(n) = A000594(n) (mod 5). See A126832 for references. - Wolfdieter Lang, Feb 03 2017

L.g.f.: Sum_{k>=1} k*x^k/(1 - x^k) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 13 2017

MATHEMATICA

# DivisorSigma[1, #]&/@Range[80]  (* Harvey P. Dale, Mar 12 2011 *)

PROG

(PARI) {a(n) = if ( n==0, 0, n * sigma(n))}

(PARI) { for (n=1, 1000, write("b064987.txt", n, " ", n*sigma(n)) ) } \\ Harry J. Smith, Oct 02 2009

(MuPad) numlib::sigma(n)*n$ n=1..81 // Zerinvary Lajos, May 13 2008

(Haskell)

a064987 n = a000203 n * n  -- Reinhard Zumkeller, Jan 21 2014

CROSSREFS

Cf. A000203, A038040, A002618, A000010, A001157, A143308, A143311, A004009, A006352, A000594, A126832.

Sequence in context: A009242 A032647 A086792 * A057341 A068412 A183026

Adjacent sequences:  A064984 A064985 A064986 * A064988 A064989 A064990

KEYWORD

mult,nonn

AUTHOR

Vladeta Jovovic, Oct 30 2001

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 12 20:04 EST 2017. Contains 295954 sequences.