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A125640
Primitive doubly abundant numbers - doubly abundant numbers that are not the multiple of another doubly abundant number.
2
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
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. A027751.
Sequence in context: A347063 A371920 A125639 * A141545 A106682 A334790
KEYWORD
nonn
AUTHOR
Gabriel Cunningham (gabriel.cunningham(AT)gmail.com), Nov 28 2006
EXTENSIONS
Data corrected by Reinhard Zumkeller, Oct 31 2015
STATUS
approved