login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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!)
A077455 a(n) = sigma_4(n^4)/sigma(n^4). 4
1, 2255, 360205, 8965359, 195688121, 812262275, 11869610005, 36654862063, 190649623129, 441276712855, 2853329308061, 3229367138595, 21506735660905, 26765970561275, 70487839624805, 150121132912367, 548357292625505, 429914900155895, 2096841596815405, 1754414256800439 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A001158(n^4)/A000203(n^4).

Multiplicative with a(p^e) = (p^(12*e+3) + p^(8*e+2) + p^(4*e+1) + 1)/(p^3 + p^2 + p + 1). - Amiram Eldar, Sep 09 2020

EXAMPLE

a(2) = sigma_4(2^4)/sigma(2^4) = 69905/31 = 2255.

MATHEMATICA

f[p_, e_] := (p^(12*e+3) + p^(8*e+2) + p^(4*e+1) + 1)/(p^3 + p^2 + p + 1); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 20] (* Amiram Eldar, Sep 09 2020 *)

PROG

(PARI) a(n)=sumdiv(n^4, d, d^4)/sigma(n^4)

(PARI) a(n) = my(f=factor(n^4)); sigma(f, 4)/sigma(f); \\ Michel Marcus, Sep 09 2020

CROSSREFS

Cf. A000203, A000583, A001158, A057660, A077454, A077456.

Sequence in context: A287701 A123297 A251944 * A068754 A222951 A035873

Adjacent sequences:  A077452 A077453 A077454 * A077456 A077457 A077458

KEYWORD

nonn,easy,mult

AUTHOR

Benoit Cloitre, Nov 30 2002

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 18 19:59 EST 2021. Contains 340262 sequences. (Running on oeis4.)