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 A091191 Primitive abundant numbers: abundant numbers (A005101) having no abundant proper divisor. 20
 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. This is a supersequence of the primitive abundant number sequence A071395, since many of these numbers will be positive integer multiples of the perfect numbers (A000396). - Timothy L. Tiffin, Jul 15 2016 If the terms of A071395 are removed from this sequence, then the resulting sequence will be A275082. - Timothy L. Tiffin, Jul 16 2016 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 EXAMPLE 12 is a term since 1, 2, 3, 4, and 6 (the proper divisors of 12) are either deficient or perfect numbers, and thus not abundant. - Timothy L. Tiffin, Jul 15 2016 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 *) Select[Range@ 840, DivisorSigma[1, #] > 2 # && Times @@ Boole@ Map[DivisorSigma[1, #] <= 2 # &, Most@ Divisors@ #] == 1 &] (* Michael De Vlieger, Jul 16 2016 *) 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), supersequence of A275082. Cf. A294930 (characteristic function), A294890. Sequence in context: A098899 A098770 A181487 * A259980 A257719 A192819 Adjacent sequences:  A091188 A091189 A091190 * A091192 A091193 A091194 KEYWORD nonn AUTHOR Reinhard Zumkeller, Dec 27 2003 STATUS approved

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