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A089371 Number of divisors of n that do not exceed the abundance of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A133886 A061859 A289110

Adjacent sequences:  A089368 A089369 A089370 * A089372 A089373 A089374

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Dec 27 2003

STATUS

approved

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Last modified September 25 21:33 EDT 2017. Contains 292500 sequences.