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A091191 Primitive abundant numbers: abundant numbers (A005101) having no abundant proper divisor. 10
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 A247625

Adjacent sequences:  A091188 A091189 A091190 * A091192 A091193 A091194

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Dec 27 2003

STATUS

approved

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Last modified December 21 18:59 EST 2014. Contains 252325 sequences.