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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A068984 a(n) = Sum_{d|n} d*tau(d)^2. 1
1, 9, 13, 45, 21, 117, 29, 173, 94, 189, 45, 585, 53, 261, 273, 573, 69, 846, 77, 945, 377, 405, 93, 2249, 246, 477, 526, 1305, 117, 2457, 125, 1725, 585, 621, 609, 4230, 149, 693, 689, 3633, 165, 3393, 173, 2025, 1974, 837, 189, 7449, 470, 2214, 897 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

Multiplicative with a(p^e) = (p^(e+3)-3*p^(e+2)+4*p^(e+1)-p-1+2*p^(e+3)*e-6*p^(e+2)*e+4*p^(e+1)*e+p^(e+3)*e^2-2*p^(e+2)*e^2+p^(e+1)*e^2)/(p-1)^3.

MATHEMATICA

a[n_] := DivisorSum[n, # * DivisorSigma[0, #]^2 &]; Array[a, 100] (* Amiram Eldar, Sep 15 2019 *)

PROG

(PARI) a(n) = sumdiv(n, d, d*numdiv(d)^2) \\ Michel Marcus, Jun 17 2013

(MAGMA [&+[d*#Divisors(d)^2: d in Divisors(n)]:n in [1..51]]; // Marius A. Burtea, Sep 15 2019

CROSSREFS

Cf. A000005, A062369, A060724, A064950.

Sequence in context: A160118 A188343 A160117 * A146016 A146128 A146039

Adjacent sequences:  A068981 A068982 A068983 * A068985 A068986 A068987

KEYWORD

mult,nonn

AUTHOR

Vladeta Jovovic, Apr 01 2002

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 8 20:11 EST 2021. Contains 349596 sequences. (Running on oeis4.)