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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A277790 Numerator of sum of reciprocals of proper divisors of n. 2
0, 1, 1, 3, 1, 11, 1, 7, 4, 17, 1, 9, 1, 23, 23, 15, 1, 19, 1, 41, 31, 35, 1, 59, 6, 41, 13, 55, 1, 71, 1, 31, 47, 53, 47, 5, 1, 59, 55, 89, 1, 95, 1, 83, 77, 71, 1, 41, 8, 46, 71, 97, 1, 119, 71, 17, 79, 89, 1, 167, 1, 95, 103, 63, 83, 13, 1, 125, 95, 143, 1, 97, 1, 113, 41, 139, 95, 167, 1, 37 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..80.

Eric Weisstein's World of Mathematics, Restricted Divisor Function

Index entries for sequences related to sums of divisors

FORMULA

a(n) = numerator(Sum_{d|n, d<n} 1/d).

a(n) = numerator((sigma_1(n)-1)/n).

a(p) = 1 for p is prime.

a(p^k) = (p^k - 1)/(p - 1) for p is prime.

Dirichlet g.f.: (zeta(s) - 1)*zeta(s+1) (for fraction Sum_{d|n, d<n} 1/d).

EXAMPLE

a(4) = 3 because 4 has 3 divisors {1,2,4} therefore 2 proper divisors {1,2} and 1/1 + 1/2 = 3/2.

0, 1, 1, 3/2, 1, 11/6, 1, 7/4, 4/3, 17/10, 1, 9/4, 1, 23/14, 23/15, 15/8, 1, 19/9, 1, 41/20, 31/21, 35/22, 1, 59/24, 6/5, 41/26, 13/9, 55/28, ...

MAPLE

with(numtheory): P:=proc(n) local a, k; a:=divisors(n) minus {n};

numer(add(1/a[k], k=1..nops(a))); end: seq(P(i), i=1..80); # Paolo P. Lava, Oct 17 2018

MATHEMATICA

Table[Numerator[DivisorSigma[-1, n] - 1/n], {n, 1, 80}]

Table[Numerator[(DivisorSigma[1, n] - 1)/n], {n, 1, 80}]

PROG

(PARI) a(n) = numerator((sigma(n)-1)/n); \\ Michel Marcus, Nov 01 2016

CROSSREFS

Cf. A000203, A001065, A017665, A017666, A277791 (denominators).

Sequence in context: A276391 A119632 A201131 * A134761 A166752 A205483

Adjacent sequences:  A277787 A277788 A277789 * A277791 A277792 A277793

KEYWORD

nonn,frac

AUTHOR

Ilya Gutkovskiy, Oct 31 2016

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 November 17 18:42 EST 2018. Contains 317276 sequences. (Running on oeis4.)