A125639 - OEIS

%I #20 Mar 11 2024 04:20:12

%S 24,30,42,54,60,66,78,84,90,96,102,114,120,126,132,138,140,150,168,

%T 174,176,180,186,198,204,210,216,222,224,234,240,246,252,258,264,270,

%U 276,280,282,294,306,308,312,318,330,340,342,348,354,360,364,366,378,380

%N Doubly abundant numbers - numbers k such that k and s(k) are abundant, where s() is A001065.

%C 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.

%H Reinhard Zumkeller, <a href="/A125639/b125639.txt">Table of n, a(n) for n = 1..10000</a>

%t 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 *)

%o (Haskell)

%o a125639 n = a125639_list !! (n-1)

%o a125639_list = filter f [1..] where

%o    f x = sx > x && a001065 sx > sx where sx = a001065 x

%o -- _Reinhard Zumkeller_, Oct 31 2015

%o (PARI) is(n)=my(s=sigma(n)); s>2*n && sigma(s-n,-1)>2 \\ _Charles R Greathouse IV_, Feb 21 2017

%Y Cf. A005101, A125640, A001065.

%K nonn

%O 1,1

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