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

1,1

Comments

Are there infinitely many primitive doubly abundant numbers?

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A005101, A125639.

Cf. A027751.

Sequence in context: A347063 A371920 A125639 * A141545 A106682 A334790

Adjacent sequences: A125637 A125638 A125639 * A125641 A125642 A125643

Keyword

nonn

Author

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

Extensions

Data corrected by Reinhard Zumkeller, Oct 31 2015

Status

approved