login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A345273 a(n) = Sum_{d|n} (n-d)^tau(d). 0
0, 1, 2, 7, 4, 30, 6, 107, 44, 98, 10, 2000, 12, 206, 258, 6035, 16, 21963, 18, 14664, 540, 542, 22, 3165444, 424, 770, 6434, 53384, 28, 544568, 30, 1403235, 1416, 1346, 1718, 225979931, 36, 1694, 2010, 65907940, 40, 2493140, 42, 301152, 860064, 2510, 46, 112291412012, 1812 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

If p is prime, a(p) = Sum_{d|p} (p-d)^tau(d) = (p-1)^1 + 0^2 = p-1.

LINKS

Table of n, a(n) for n=1..49.

EXAMPLE

a(10) = Sum_{d|10} (10-d)^tau(d) = 9^1 + 8^2 + 5^2 + 0^4 = 9 + 64 + 25 = 98.

MATHEMATICA

Table[Sum[(n - k)^DivisorSigma[0, k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 50}]

CROSSREFS

Cf. A000005 (tau), A174937.

Sequence in context: A190716 A303384 A013623 * A348145 A210421 A326098

Adjacent sequences:  A345270 A345271 A345272 * A345274 A345275 A345276

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jun 12 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)