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!)
A000082 a(n) = n^2*Product_{p|n} (1 + 1/p). 8
1, 6, 12, 24, 30, 72, 56, 96, 108, 180, 132, 288, 182, 336, 360, 384, 306, 648, 380, 720, 672, 792, 552, 1152, 750, 1092, 972, 1344, 870, 2160, 992, 1536, 1584, 1836, 1680, 2592, 1406, 2280, 2184, 2880, 1722, 4032, 1892, 3168, 3240, 3312, 2256 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For n > 1: A006530(a(n)) = A076566(n-1). - Reinhard Zumkeller, Oct 03 2012

A strong divisibility sequence, that is, gcd(a(n), a(m)) = a(gcd(n, m)) for all positive integers n and m. - Michael Somos, Jan 01 2017

REFERENCES

B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, p. 79.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Index to divisibility sequences

FORMULA

Dirichlet g.f.: zeta(s-1)*zeta(s-2)/zeta(2*s-2).

Dirichlet convolution: Sum_{d|n} mu(n/d)*sigma(d^2). - Vladeta Jovovic, Nov 16 2001

Multiplicative with a(p^e) = p^(2*e-1)*(p+1). - David W. Wilson, Aug 01 2001

a(n) = A181797(n)*A003557(n). - R. J. Mathar, Mar 30 2011

a(n) = A001615(n^2). - Enrique Pérez Herrero, Mar 06 2012

MAPLE

proc(n) local b, d: b := n^2: for d from 1 to n do if irem(n, d) = 0 and isprime(d) then b := b*(1+d^(-1)): fi: od: RETURN(b): end:

MATHEMATICA

Table[ Fold[ If[ Mod[ n, #2 ]==0 && PrimeQ[ #2 ], #1*(1+1/#2), #1 ]&, n^2, Range[ n ] ], {n, 1, 45} ]

Table[ n^2 Times@@(1+1/Select[ Range[ 1, n ], (Mod[ n, #1 ]==0&&PrimeQ[ #1 ])& ]), {n, 1, 45} ] (*Olivier Gérard, Aug 15 1997 *)

PROG

(PARI) a(n)=if(n<1, 0, direuler(p=2, n, (1+p*X)/(1-p^2*X))[n])

(Haskell)

a000082 n = product $ zipWith (\p e -> p ^ (2*e - 1) * (p + 1))

                              (a027748_row n) (a124010_row n)

-- Reinhard Zumkeller, Oct 03 2012

CROSSREFS

a(n) = n*A001615(n). Cf. A033196.

Cf. A027748, A124010.

Sequence in context: A119500 A260633 A110967 * A263849 A227416 A106697

Adjacent sequences:  A000079 A000080 A000081 * A000083 A000084 A000085

KEYWORD

nonn,easy,nice,mult

AUTHOR

N. J. A. Sloane

EXTENSIONS

Additional comments from Michael Somos, May 19 2000

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 13 17:30 EST 2017. Contains 295959 sequences.