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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A017669 Numerator of sum of -3rd powers of divisors of n. 3
1, 9, 28, 73, 126, 7, 344, 585, 757, 567, 1332, 511, 2198, 387, 392, 4681, 4914, 757, 6860, 4599, 1376, 2997, 12168, 455, 15751, 9891, 20440, 3139, 24390, 147, 29792, 37449, 4144, 22113, 6192, 55261, 50654, 15435, 61544, 7371, 68922, 172, 79508, 24309, 10598 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)

FORMULA

Numerators of coefficients in expansion of Sum_{k>=1} x^k/(k^3*(1 - x^k)). - Ilya Gutkovskiy, May 24 2018

EXAMPLE

1, 9/8, 28/27, 73/64, 126/125, 7/6, 344/343, 585/512, 757/729, 567/500, 1332/1331, 511/432, ...

MATHEMATICA

Table[Numerator[DivisorSigma[-3, n]], {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2011 *)

Table[Numerator[DivisorSigma[3, n]/n^3], {n, 1, 40}] (* G. C. Greubel, Nov 08 2018 *)

PROG

(PARI) vector(40, n, numerator(sigma(n, 3)/n^3)) \\ G. C. Greubel, Nov 08 2018

(MAGMA) [Numerator(DivisorSigma(3, n)/n^3): n in [1..40]]; // G. C. Greubel, Nov 08 2018

CROSSREFS

Cf. A017670.

Sequence in context: A062451 A065959 A226333 * A277065 A001158 A171215

Adjacent sequences:  A017666 A017667 A017668 * A017670 A017671 A017672

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane

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 December 5 15:11 EST 2019. Contains 329753 sequences. (Running on oeis4.)