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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A065958 a(n) = n^2*Product_{distinct primes p dividing n} (1+1/p^2). 11
1, 5, 10, 20, 26, 50, 50, 80, 90, 130, 122, 200, 170, 250, 260, 320, 290, 450, 362, 520, 500, 610, 530, 800, 650, 850, 810, 1000, 842, 1300, 962, 1280, 1220, 1450, 1300, 1800, 1370, 1810, 1700, 2080, 1682, 2500, 1850, 2440, 2340, 2650, 2210 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence is considered to be psi_2, a generalization of Dedekind Psi Function, where psi_1 is A001615. - Enrique Pérez Herrero, Jul 06 2011

REFERENCES

József Sándor, Geometric Theorems, Diophantine Equations, and Arithmetic Functions, American Research Press, Rehoboth 2002, pp. 193.

LINKS

E. Pérez Herrero, Table of n, a(n) for n = 1..10000

F. A. Lewis and others, Problem 4002, Amer. Math. Monthly, Vol. 49, No. 9, Nov. 1942, pp. 618-619.

FORMULA

Multiplicative with a(p^e) = p^(2*e) + p^(2*e-2). - Vladeta Jovovic, Dec 09 2001

a(n) = n^2*sum(d|n, mu(d)^2/d^2) - Benoit Cloitre, Apr 07 2002

a(n) = sum(d|n, mu(d)^2*d^2). - Joerg Arndt, Jul 06 2011

Inverse Euler transform of n*A156733(n). - Paul D. Hanna and Vladeta Jovovic, Feb 14 2009

From Enrique Pérez Herrero, Aug 22 2010: (Start)

a(n) = J_4(n)/(phi(n)*psi(n)) = A059377(n)/(A001615(n)*A000010(n))

a(n) = J_4(n)/J_2(n) = A059377(n)/A007434(n), where J_k is the k-th Jordan Totient Function. (End)

Dirichlet g.f.: zeta(s)*zeta(s-2)/zeta(2s). Dirichlet convolution of A008966 and A000290. - R. J. Mathar, Apr 10 2011

G.f.: Sum_{k>=1} mu(k)^2*x^k*(1 + x^k)/(1 - x^k)^3. - Ilya Gutkovskiy, Oct 24 2018

MAPLE

A065958 := proc(n) local i, j, k, t1, t2, t3; t1 := ifactors(n)[2]; t2 := n^2*mul((1+1/(t1[i][1])^2), i=1..nops(t1)); end;

MATHEMATICA

JordanTotient[n_, k_:1]:=DivisorSum[n, #^k*MoebiusMu[n/# ]&]/; (n>0)&&IntegerQ[n]; A065958[n_]:=JordanTotient[n, 4]/JordanTotient[n, 2]; (* Enrique Pérez Herrero, Aug 22 2010 *)

PROG

(PARI) for(n=1, 100, print1(n*sumdiv(n, d, moebius(d)^2/d^2), ", "))

(PARI) a(n)=sumdiv(n, d, moebius(n/d)^2*d^2); /* Joerg Arndt, Jul 06 2011 */

CROSSREFS

Cf. A000010, A001615, A007434, A065959, A065960, A156733, A301978, A301980.

Sequence in context: A072703 A086761 A045191 * A065969 A027884 A236391

Adjacent sequences:  A065955 A065956 A065957 * A065959 A065960 A065961

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Dec 08 2001

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 January 20 02:13 EST 2019. Contains 319320 sequences. (Running on oeis4.)