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.

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, 9, 9, 8, 10, 10, 10, 10, 10, 12, 11, 9, 12, 11, 11, 14, 10, 14, 14, 13, 14, 13, 13, 14, 16, 15, 13, 16, 15, 17, 17, 15, 18, 14, 17, 16, 19, 18, 19, 15, 20, 19, 18, 20, 20, 18, 20, 21, 22

Offset: 1

Author

Jason Earls, Jun 08 2003

Keywords

• easy
• nonn

Examples

			Triangle begins
1 (0 abundant)
2 3 (0 abundant)
4 5 6 (0 abundant)
7 8 9 10 (0 abundant)
11 12 13 14 15 (1 abundant)
16 17 18 19 20 21 (2 abundant)
22 23 24 25 26 27 28 (1 abundant)
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000217, A005101, A091194, A294937.

Programs

Maple

f:= proc(n) local i;
      nops(select(t -> numtheory:-sigma(t) > 2*t, [$(n-1)*n/2+1 .. n*(n+1)/2]))
end proc:
map(f, [$1..100]); # Robert Israel, Aug 13 2024

Mathematica

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 *)

Formula

a(n) = A091194(A000217(n)) - A091194(A000217(n-1)). - Robert Israel, Aug 13 2024