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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A060326 Numbers n such that 2*n - sigma(n) is a divisor of n and greater than one, where sigma = A000203 is the sum of divisors. 2
10, 44, 136, 152, 184, 752, 884, 2144, 2272, 2528, 8384, 12224, 17176, 18632, 18904, 32896, 33664, 34688, 49024, 63248, 85936, 106928, 116624, 117808, 526688, 527872, 531968, 556544, 589312, 599072, 654848, 709784, 801376, 879136, 885928, 1090912 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For n=2^k, sigma(n)=2n-1, so that 2n-sigma(n)=1 would trivially divide n. These n are excluded. All abundant numbers (with sigma(n)>2n) are also excluded, even when sigma(n)-2n divides n, as for n=12 which is a multiple of 2n-sigma(n) = -4. - M. F. Hasler, Jul 21 2012

The sequence can also be obtained by looking for numbers whose abundancy sigma(n)/n with form (2*k-1)/k (hence deficient), while excluding powers of 2. - Michel Marcus, Oct 07 2013

LINKS

R. J. Mathar and Donovan Johnson, Table of n, a(n) for n = 1..200 (first 42 terms from R. J. Mathar)

FORMULA

{ m in A005100 \ A000079 : A033879(m) divides m }.  - M. F. Hasler, Jul 21 2012

EXAMPLE

10 is a member because the divisors of 10 are 1,2,5,10, with sum 18 and 2*n-18 = 2, which divides 10. Or sigma(10)/10 = 9/5 = (2*k-1)/k with k=5.

MATHEMATICA

sdnQ[n_]:=Module[{c=2n-DivisorSigma[1, n]}, c>1&&Divisible[n, c]]; Select[ Range[600000], sdnQ] (* Harvey P. Dale, Jul 23 2012 *)

PROG

(PARI) for(n=1, 6e5, (t=2*n-sigma(n))>1 & !(n%t) & print1(n", "))  \\ - M. F. Hasler, Jul 21 2012

CROSSREFS

Cf. A214408.

Sequence in context: A085582 A058310 A005720 * A200448 A124852 A220923

Adjacent sequences:  A060323 A060324 A060325 * A060327 A060328 A060329

KEYWORD

nonn

AUTHOR

Phil Mason (hattrack(AT)usa.net)

EXTENSIONS

More terms from Michel Marcus, Oct 07 2013

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 September 17 06:52 EDT 2019. Contains 327119 sequences. (Running on oeis4.)