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A125639
Doubly abundant numbers - numbers k such that k and s(k) are abundant, where s() is A001065.
5
24, 30, 42, 54, 60, 66, 78, 84, 90, 96, 102, 114, 120, 126, 132, 138, 140, 150, 168, 174, 176, 180, 186, 198, 204, 210, 216, 222, 224, 234, 240, 246, 252, 258, 264, 270, 276, 280, 282, 294, 306, 308, 312, 318, 330, 340, 342, 348, 354, 360, 364, 366, 378, 380
OFFSET
1,1
COMMENTS
Unlike abundant numbers, not all multiples of doubly abundant numbers are doubly abundant; for instance, 48 is not doubly abundant. There are infinitely many doubly abundant numbers; for instance, all numbers of the form 24*25^k are doubly abundant. Such a number is abundant, being a multiple of an abundant number and s(24*25^k) = s(24)*s(25^k) + 24*s(25^k) + 25^k*s(24), which is a multiple of s(24) = 36.
LINKS
MATHEMATICA
s[n_] := DivisorSigma[1, n] - n; q[n_] := Module[{s1 = s[n]}, s1 > n && s[s1] > s1]; Select[Range[400], q] (* Amiram Eldar, Mar 11 2024 *)
PROG
(Haskell)
a125639 n = a125639_list !! (n-1)
a125639_list = filter f [1..] where
f x = sx > x && a001065 sx > sx where sx = a001065 x
-- Reinhard Zumkeller, Oct 31 2015
(PARI) is(n)=my(s=sigma(n)); s>2*n && sigma(s-n, -1)>2 \\ Charles R Greathouse IV, Feb 21 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Gabriel Cunningham (gabriel.cunningham(AT)gmail.com), Nov 28 2006
STATUS
approved