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A084840 Write the numbers 1, 2, ... in a triangle with n terms in the n-th row; a(n) = number of abundant integers in n-th row.

%I A084840 #13 Jan 27 2025 19:24:44
%S A084840 0,0,0,0,1,2,1,2,2,2,3,3,4,4,4,2,4,4,4,7,5,4,6,5,7,6,8,7,6,9,7,8,9,8,
%T A084840 9,9,8,10,10,10,10,10,12,11,9,12,11,11,14,10,14,14,13,14,13,13,14,16,
%U A084840 15,13,16,15,17,17,15,18,14,17,16,19,18,19,15,20,19,18,20,20,18,20,21,22
%N A084840 Write the numbers 1, 2, ... in a triangle with n terms in the n-th row; a(n) = number of abundant integers in n-th row.
%H A084840 Robert Israel, <a href="/A084840/b084840.txt">Table of n, a(n) for n = 1..2000</a>
%F A084840 a(n) = A091194(A000217(n)) - A091194(A000217(n-1)). - _Robert Israel_, Aug 13 2024
%e A084840 Triangle begins
%e A084840 1 (0 abundant)
%e A084840 2 3 (0 abundant)
%e A084840 4 5 6 (0 abundant)
%e A084840 7 8 9 10 (0 abundant)
%e A084840 11 12 13 14 15 (1 abundant)
%e A084840 16 17 18 19 20 21 (2 abundant)
%e A084840 22 23 24 25 26 27 28 (1 abundant)
%p A084840 f:= proc(n) local i;
%p A084840       nops(select(t -> numtheory:-sigma(t) > 2*t, [$(n-1)*n/2+1 .. n*(n+1)/2]))
%p A084840 end proc:
%p A084840 map(f, [$1..100]); # _Robert Israel_, Aug 13 2024
%t A084840 nai[lst_]:=Count[lst,_?(DivisorSigma[1,#]-2#>0&)]; Module[{nn=90,tbl},tbl=TakeList[Range[(nn(nn+1))/2],Range[nn]];nai/@tbl] (* _Harvey P. Dale_, Jan 27 2025 *)
%Y A084840 Cf. A000217, A005101, A091194, A294937.
%K A084840 easy,nonn
%O A084840 1,6
%A A084840 _Jason Earls_, Jun 08 2003