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

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A059376 Jordan function J_3(n). 26
1, 7, 26, 56, 124, 182, 342, 448, 702, 868, 1330, 1456, 2196, 2394, 3224, 3584, 4912, 4914, 6858, 6944, 8892, 9310, 12166, 11648, 15500, 15372, 18954, 19152, 24388, 22568, 29790, 28672, 34580, 34384, 42408, 39312, 50652, 48006, 57096 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 199, #3.

R. Sivaramakrishnan, "The many facets of Euler's totient. II. Generalizations and analogues", Nieuw Arch. Wisk. (4) 8 (1990), no. 2, 169-187.

LINKS

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

FORMULA

Multiplicative with a(p^e) = p^(3e)-p^(3e-3). - Vladeta Jovovic, Jul 26 2001

a(n)=sum(d|n, d^3*mu(n/d)) - Benoit Cloitre, Apr 05 2002

Dirichlet generating function: zeta(s-3)/zeta(s). - Franklin T. Adams-Watters, Sep 11 2005

A063453(n) divides a(n). - R. J. Mathar, Mar 30 2011

a(n) = Sum_{k=1..n} GCD(k,n)^3 * Cos(2*Pi*k/n). - Enrique Pérez Herrero, Jan 18 2013

MAPLE

J := proc(n, k) local i, p, t1, t2; t1 := n^k; for p from 1 to n do if isprime(p) and n mod p = 0 then t1 := t1*(1-p^(-k)); fi; od; t1; end; # (with k = 3)

MATHEMATICA

JordanJ[n_, k_: 1] := DivisorSum[n, #^k*MoebiusMu[n/#] &]; f[n_] := JordanJ[n, 3]; Array[f, 39]

PROG

(PARI) for(n=1, 120, print1(sumdiv(n, d, d^3*moebius(n/d)), ", "))

(PARI) for (n = 1, 1000, write("b059376.txt", n, " ", sumdiv(n, d, d^3*moebius(n/d))); ) \\ Harry J. Smith, Jun 26 2009

(PARI) a(n)=sumdivmult(n, d, d^3*moebius(n/d)) \\ Charles R Greathouse IV, Sep 09 2014

CROSSREFS

See A059379 and A059380 (triangle of values of J_k(n)), A000010 (J_1), A059376 (J_3), A059377 (J_4), A059378 (J_5).

Sequence in context: A063153 A063578 A063159 * A206481 A049453 A231888

Adjacent sequences:  A059373 A059374 A059375 * A059377 A059378 A059379

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Jan 28 2001

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 27 14:29 EST 2014. Contains 250210 sequences.