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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A035316 Sum of square divisors of n. 21
1, 1, 1, 5, 1, 1, 1, 5, 10, 1, 1, 5, 1, 1, 1, 21, 1, 10, 1, 5, 1, 1, 1, 5, 26, 1, 10, 5, 1, 1, 1, 21, 1, 1, 1, 50, 1, 1, 1, 5, 1, 1, 1, 5, 10, 1, 1, 21, 50, 26, 1, 5, 1, 10, 1, 5, 1, 1, 1, 5, 1, 1, 10, 85, 1, 1, 1, 5, 1, 1, 1, 50, 1, 1, 26, 5, 1, 1, 1, 21, 91, 1, 1, 5, 1, 1, 1, 5, 1, 10, 1, 5, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The Dirichlet generating function is zeta(s)*zeta(2s-2). The sequence is the Dirichlet convolution of A000012 with the sequence defined by n*A010052(n). - R. J. Mathar, Feb 18 2011

LINKS

Nick Hobson, Table of n, a(n) for n = 1..1000

Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

FORMULA

Multiplicative with a(p^e)=(p^(e+2)-1)/(p^2-1) for even e and a(p^e)=(p^(e+1)-1)/(p^2-1) for odd e. - Vladeta Jovovic, Dec 05 2001

G.f.: Sum_{k>0} k^2*x^(k^2)/(1-x^(k^2)). - Vladeta Jovovic, Dec 13 2002

a(n^2) = A001157(n). - Michel Marcus, Jan 14 2014

MATHEMATICA

Table[ Plus @@ Select[ Divisors@ n, IntegerQ@ Sqrt@ # &], {n, 93}] (* Robert G. Wilson v, Feb 19 2011 *)

PROG

(PARI) vector(93, n, sumdiv(n, d, issquare(d)*d))

(PARI) a(n)=my(f=factor(n)); prod(i=1, #f[, 1], (f[i, 1]^(f[i, 2]+2-f[i, 2]%2)-1)/(f[i, 1]^2-1)) \\ Charles R Greathouse IV, May 20 2013

(Haskell)

a035316 n = product $

   zipWith (\p e -> (p ^ (e + 2 - mod e 2) - 1) `div` (p ^ 2 - 1))

           (a027748_row n) (a124010_row n)

-- Reinhard Zumkeller, Jul 28 2014

CROSSREFS

Cf. A000012, A001157, A010052, A046951, A027748, A124010.

Sequence in context: A100615 A222119 A102280 * A068316 A284252 A284254

Adjacent sequences:  A035313 A035314 A035315 * A035317 A035318 A035319

KEYWORD

nonn,mult,changed

AUTHOR

N. J. A. Sloane.

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 April 25 14:30 EDT 2017. Contains 285414 sequences.