The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A080224 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A080224

Number of abundant divisors of n.
(history; published version)

#20 by R. J. Mathar at Mon Feb 22 11:43:54 EST 2021

STATUS

editing

approved

#19 by R. J. Mathar at Mon Feb 22 11:43:46 EST 2021

MAPLE

A080224 := proc(n)

a := 0 ;

for d in numtheory[divisors](n) do

if numtheory[sigma](d) > 2*d then

a := a+1 ;

end if;

end do:

a;

end proc:

seq(A080224(n), n=1..80) ; # R. J. Mathar, Feb 22 2021

STATUS

approved

editing

#18 by N. J. A. Sloane at Tue Nov 14 17:10:50 EST 2017

STATUS

proposed

approved

#17 by Antti Karttunen at Tue Nov 14 15:44:27 EST 2017

STATUS

editing

proposed

#16 by Antti Karttunen at Tue Nov 14 15:09:03 EST 2017

FORMULA

a(n) = Sum_{d|n} A294937(d) = A294929(n) + A294937(n).

a(n) = A294929(n) + A294937(n).

a(n) = 1 iff A294930(n) = 1.

CROSSREFS

Cf. A000005, A000203, A005101, A080225, A080226, A187795, A294890, A294929, A294930, A294937.

#15 by Antti Karttunen at Tue Nov 14 14:49:01 EST 2017

CROSSREFS

Cf. A000005, A000203, A005101, A080225, A080226, A187795, A294890, A294929, A294937.

#14 by Antti Karttunen at Tue Nov 14 13:18:03 EST 2017

CROSSREFS

Cf. also A294904.

#13 by Antti Karttunen at Tue Nov 14 13:01:27 EST 2017

COMMENTS

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

FORMULA

a(n) + A080225(n) + A080226(n) = A000005(n).

From Antti Karttunen, Nov 14 2017: (Start)

a(n) = Sum_{d|n} A294937(d) = A294929(n) + A294937(n).

(End)

CROSSREFS

Cf. A005101, A000005, A000203, A005101, A080225, A080226, A187795, A294929, A294937.

STATUS

approved

editing

#12 by Harvey P. Dale at Fri Jun 14 15:00:56 EDT 2013

STATUS

editing

approved

#11 by Harvey P. Dale at Fri Jun 14 15:00:49 EDT 2013

MATHEMATICA

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

STATUS

approved

editing