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A080224 Number of abundant divisors of n. 8
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 5, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 3, 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,24

COMMENTS

Number of divisors d of n with sigma(d)>2*d (sigma=A000203); a(n)+A080225(n)+A080226(n)=A000005(n).

a(n)>0 iff n is abundant: a(A005101(n))>0, a(A000396(n))=0 and a(A005100(n))=0; a(A091191(n))=1; a(A091192(n))>1; a(A091193(n))=n and a(m)<>n for m < A091193(n). - Reinhard Zumkeller, Dec 27 2003

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Abundant Number.

EXAMPLE

Divisors of n=24: {1,2,3,4,6,8,12,24}, two of them are abundant: 12=A005101(1) and 24=A005101(4), therefore a(24)=2.

MATHEMATICA

Table[Count[Divisors[n], _?(DivisorSigma[1, #]>2#&)], {n, 110}] (* Harvey P. Dale, Jun 14 2013 *)

PROG

(PARI) a(n) = sumdiv(n, d, sigma(d)>2*d)  \\ Michel Marcus, Mar 09 2013

CROSSREFS

Cf. A005101, A000203.

Sequence in context: A122841 A060862 A066087 * A261488 A010105 A083916

Adjacent sequences:  A080221 A080222 A080223 * A080225 A080226 A080227

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 07 2003

STATUS

approved

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Last modified March 28 05:07 EDT 2017. Contains 284182 sequences.