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

 

Logo

Invitation: celebrating 50 years of OEIS, 250000 sequences, and Sloane's 75th, there will be a conference at DIMACS, Rutgers, Oct 9-10 2014.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A091191 Primitive abundant numbers: abundant numbers (A005101) having no abundant proper divisor. 9
12, 18, 20, 30, 42, 56, 66, 70, 78, 88, 102, 104, 114, 138, 174, 186, 196, 222, 246, 258, 272, 282, 304, 308, 318, 354, 364, 366, 368, 402, 426, 438, 464, 474, 476, 498, 532, 534, 550, 572, 582, 606, 618, 642, 644, 650, 654, 678, 748, 762, 786, 812, 822 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A080224(a(n))=1.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

P. Erdős, On the density of the abundant numbers, J. London Math. Soc. 9 (1934), pp. 278-282.

Eric Weisstein's World of Mathematics, Abundant Number

FORMULA

Erdős shows that a(n) >> n log^2 n. - Charles R Greathouse IV, Dec 05 2012

MAPLE

isA005101 := proc(n) is(numtheory[sigma](n) > 2*n ); end proc:

isA091191 := proc(n) local d; if isA005101(n) then for d in numtheory[divisors](n) minus {1, n} do if isA005101(d) then return false; end if; end do: return true; else false; end if; end proc:

for n from 1 to 200 do if isA091191(n) then printf("%d\n", n) ; end if; end do: # R. J. Mathar, Mar 28 2011

MATHEMATICA

t = {}; n = 1; While[Length[t] < 100, n++; If[DivisorSigma[1, n] > 2*n && Intersection[t, Divisors[n]] == {}, AppendTo[t, n]]]; t (* T. D. Noe, Mar 28 2011 *)

PROG

(PARI) is(n)=sumdiv(n, d, sigma(d, -1)>2)==1 \\ Charles R Greathouse IV, Dec 05 2012

(Haskell)

a091191 n = a091191_list !! (n-1)

a091191_list = filter f [1..] where

   f x = sum pdivs > x && all (<= 0) (map (\d -> a000203 d - 2 * d) pdivs)

         where pdivs = a027751_row x

-- Reinhard Zumkeller, Jan 31 2014

CROSSREFS

Cf. A006038 (odd terms), A005101 (abundant numbers), A091192.

Cf. A027751, A071395 (subsequence).

Sequence in context: A098899 A098770 A181487 * A192819 A071927 A171674

Adjacent sequences:  A091188 A091189 A091190 * A091192 A091193 A091194

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Dec 27 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified September 20 01:15 EDT 2014. Contains 246982 sequences.