A125640 Primitive doubly abundant numbers - doubly abundant numbers that are not the multiple of another doubly abundant number.

24, 30, 42, 54, 66, 78, 102, 114, 138, 140, 174, 176, 186, 222, 224, 246, 258, 282, 308, 318, 340, 354, 364, 366, 380, 402, 426, 438, 440, 474, 476, 498, 520, 532, 534, 580, 582, 606, 618, 642, 644, 654, 678, 762, 786, 812, 822, 834, 868, 894

Offset: 1

Author

Gabriel Cunningham (gabriel.cunningham(AT)gmail.com), Nov 28 2006

Keywords

• nonn

Comments

Are there infinitely many primitive doubly abundant numbers?

Examples

			42 is a primitive doubly abundant number because it is abundant (s(42) = 54), the sum of its proper divisors is abundant (s(54) = 66) and no divisor of 42 is doubly abundant.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005101, A125639.

Cf. A027751.

Programs

Haskell

import Data.List (intersect)
a125640 n = a125640_list !! (n-1)
a125640_list = f a125639_list [] where
   f (x:xs) ys = if null (a027751_row' x `intersect` ys)
                    then x : f xs (x : ys) else f xs ys
-- Reinhard Zumkeller, Oct 31 2015

Mathematica

s[n_] := DivisorSigma[1, n] - n; q[n_] := Module[{s1 = s[n]}, s1 > n && s[s1] > s1]; primQ[n_] := q[n] && !AnyTrue[Most[Divisors[n]], q]; Select[Range[900], primQ] (* Amiram Eldar, Mar 11 2024 *)

Extensions

Data corrected by Reinhard Zumkeller, Oct 31 2015