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%I #33 Jan 28 2016 11:06:44
%S 4,6,8,9,10,12,14,15,16,18,20,21,22,24,26,27,28,30,32,33,34,35,36,38,
%T 39,40,42,44,45,46,48,49,50,51,52,54,55,56,57,58,60,62,63,64,65,66,68,
%U 69,70,72,74,75,76,77,78,80,81,82,84,85,86,87,88,90,91,92,93,94,96,98,99,100,102,104,105,106,108,110,112,114,115,116,117,118,120
%N A000120-abundant numbers.
%C Definition see in A175522. All even numbers > 2 are in the sequence.
%C A192895(a(n)) > 0. _Reinhard Zumkeller_, Jul 12 2011
%H Reinhard Zumkeller (first 1000 terms) & Antti Karttunen, <a href="/A175526/b175526.txt">Table of n, a(n) for n = 1..10000</a>
%p isA175526 := proc(n) s := 0 ; for d in (numtheory[divisors](n) minus {n}) do s := s+A000120(d) ; end do: evalb(s> A000120(n)) ; end proc:
%p for n from 1 to 120 do if isA175526(n) then printf("%d,",n); end if; end do: # _R. J. Mathar_, Jul 11 2011
%t okQ[n_] := DivisorSum[n, Total[IntegerDigits[#, 2]]*(-1)^Boole[#==n]&]>0; Select[Range[120], okQ] (* _Jean-François Alcover_, Dec 06 2015 *)
%o (Sage)
%o is_A175526 = lambda x: sum(A000120(d) for d in divisors(x)) > 2*A000120(x)
%o A175526 = filter(is_A175526, IntegerRange(1, 10**4))
%o # _D. S. McNeil_, Dec 04 2010
%o (Haskell)
%o import Data.List (findIndices)
%o a175526 n = a175526_list !! (n-1)
%o a175526_list = map (+ 1) $ findIndices (> 0) a192895_list
%o -- _Reinhard Zumkeller_, Jul 12 2011
%o (PARI)
%o A192895(n) = sumdiv(n, d, hammingweight(d)*(-1)^(d==n)); \\ _Charles R Greathouse IV_, Feb 07 2013
%o isA175526(n) = (A192895(n) > 0);
%o n = 0; i = 0; while(i < 10000, n++; if(isA175526(n), i++; write("b175526.txt", i, " ", n)));
%o \\ _Antti Karttunen_, May 11 2015
%o (PARI) is(n)=sumdiv(n,d,hammingweight(d))>2*hammingweight(n) \\ _Charles R Greathouse IV_, Jan 28 2016
%Y Cf. A175522 (perfect version), A175524 (deficient version), A257691 (complement, non-abundant version).
%Y Cf. A000120, A192895.
%Y Cf. also A005100, A005101.
%Y a(n) differs from A091212(n) and from A205783(n+1) for the first time at n=37, where a(37) = 55, while 55 is missing from both A091212 and A205783.
%Y Differs from A192506 for the first time at n=54, where a(54) = 77, while 77 is missing from A192506.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Dec 03 2010
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