A089371 Number of divisors of n that do not exceed the abundance of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 7, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 8, 0, 0, 0, 6, 0, 5, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 5, 0, 5, 0, 0, 0, 11, 0, 0, 0, 0, 0, 5, 0, 0, 0, 2, 0, 11, 0, 0, 0, 0, 0, 4, 0, 8, 0, 0, 0, 11, 0, 0, 0, 3, 0, 11, 0, 0, 0, 0, 0, 11, 0, 0, 0, 5

Offset

1,12

Comments

a(n) = #{d>0: d <= A033880(n) and n mod d = 0};

a(A005101(n))>0, a(A000396(n))=a(A005100(n))=0.

Links

Matthew House, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Abundance

Maple

f:= proc(n) local r;
  r:= numtheory:-sigma(n) - 2*n;
  if r <= 0 then 0
  else nops(select(`<=`, numtheory:-divisors(n), r))
  fi
end proc:
map(f, [$1..100]); # Robert Israel, Jul 27 2015

Mathematica

Table[Count[Divisors@ n, x_ /; x <= DivisorSigma[1, n] - 2 n], {n,
120}] (* Michael De Vlieger, Jul 27 2015 *)

Prog

(PARI) a(n) = my(ab = sigma(n) - 2*n); sumdiv(n, d, d <= ab); \\ Michel Marcus, Jul 27 2015

Crossrefs

Cf. A000005, A000203, A000396, A001065, A005100, A005101, A033880.

Sequence in context: A180989 A075444 A280492 * A318679 A133886 A061859

Adjacent sequences: A089368 A089369 A089370 * A089372 A089373 A089374

Keyword

nonn

Author

Reinhard Zumkeller, Dec 27 2003

Status

approved