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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A284650 Denominator of sum of reciprocals of all divisors of all positive integers <= n. 1
1, 2, 6, 12, 60, 60, 420, 840, 2520, 504, 5544, 5544, 72072, 72072, 360360, 720720, 12252240, 12252240, 232792560, 232792560, 232792560, 232792560, 5354228880, 5354228880, 26771144400, 26771144400, 80313433200, 80313433200, 2329089562800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..29.

Index entries for sequences related to sums of divisors

FORMULA

G.f.: (1/(1 - x))*Sum_{k>=1} log(1/(1 - x^k)) (for A284648(n)/a(n), see example).

a(n) = denominator of Sum_{k=1..n} Sum_{d|k} 1/d.

a(n) = denominator of Sum_{k=1..n} sigma(k)/k.

EXAMPLE

1, 5/2, 23/6, 67/12, 407/60, 527/60, 4169/420, 9913/840, 33379/2520, 7583/504, 89461/5544, 102397/5544, 1408777/72072, 1532329/72072, 8238221/360360, ...

MATHEMATICA

Table[Denominator[Sum[DivisorSigma[-1, k], {k, 1, n}]], {n, 1, 29}]

Table[Denominator[Sum[DivisorSigma[1, k]/k, {k, 1, n}]], {n, 1, 29}]

nmax = 29; Rest[Denominator[CoefficientList[Series[1/(1 - x) Sum[Log[1/(1 - x^k)], {k, 1, nmax}], {x, 0, nmax}], x]]]

PROG

(PARI) for(n=1, 29, print1(denominator(sum(k=1, n, sigma(k)/k)), ", ")) \\ Indranil Ghosh, Mar 31 2017

(Python)

from fractions import Fraction

from sympy import divisor_sigma

print [Fraction(str(sum([divisor_sigma(k)/k for k in xrange(1, n + 1)]))).denominator for n in xrange(1, 30)] # Indranil Ghosh, Mar 31 2017

CROSSREFS

Cf. A000203, A017665, A017666, A108775, A284648 (numerators).

Sequence in context: A117481 A083268 A225628 * A085911 A211418 A058312

Adjacent sequences:  A284647 A284648 A284649 * A284651 A284652 A284653

KEYWORD

nonn,frac

AUTHOR

Ilya Gutkovskiy, Mar 31 2017

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 24 18:24 EST 2018. Contains 299628 sequences. (Running on oeis4.)