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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A053826 Dirichlet inverse of sigma_4 function (A001159). 5
1, -17, -82, 16, -626, 1394, -2402, 0, 81, 10642, -14642, -1312, -28562, 40834, 51332, 0, -83522, -1377, -130322, -10016, 196964, 248914, -279842, 0, 625, 485554, 0, -38432, -707282, -872644, -923522, 0, 1200644, 1419874, 1503652, 1296, -1874162 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

sigma_4(n) is the sum of the 4th powers of the divisors of n (A001159).

REFERENCES

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 39.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

FORMULA

Dirichlet g.f.: 1/(zeta(x)zeta(x-4))

Multiplicative with a(p^1) = -1 - p^4, a(p^2) = p^4, a(p^e) = 0 for e>=3. - Mitch Harris, Jun 27 2005

a(n) = Sum_{d|n} mu(n/d)*mu(d)*d^4. - Ilya Gutkovskiy, Nov 06 2018

MATHEMATICA

Table[DivisorSum[n, MoebiusMu[n/#]*MoebiusMu[#]*#^4  &], {n, 1, 50}] (* G. C. Greubel, Nov 07 2018 *)

PROG

(PARI) a(n) = sumdiv(n, d, moebius(n/d)*moebius(d)*d^4); \\ Michel Marcus, Nov 06 2018

CROSSREFS

Cf. A001159, A046099 (where a(n)=0).

Sequence in context: A044204 A044585 A197397 * A184982 A088687 A321560

Adjacent sequences:  A053823 A053824 A053825 * A053827 A053828 A053829

KEYWORD

sign,mult

AUTHOR

N. J. A. Sloane, Apr 08 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 20 14:21 EDT 2019. Contains 325185 sequences. (Running on oeis4.)