login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A080226 Number of deficient divisors of n. 9
1, 2, 2, 3, 2, 3, 2, 4, 3, 4, 2, 4, 2, 4, 4, 5, 2, 4, 2, 5, 4, 4, 2, 5, 3, 4, 4, 5, 2, 6, 2, 6, 4, 4, 4, 5, 2, 4, 4, 6, 2, 6, 2, 6, 6, 4, 2, 6, 3, 6, 4, 6, 2, 5, 4, 6, 4, 4, 2, 7, 2, 4, 6, 7, 4, 6, 2, 6, 4, 7, 2, 6, 2, 4, 6, 6, 4, 6, 2, 7, 5, 4, 2, 7, 4, 4, 4, 7, 2, 8, 4, 6, 4, 4, 4, 7, 2, 6, 6, 7, 2, 6, 2, 7, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Number of divisors d of n with sigma(d)<2*d (sigma = A000203).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Eric Weisstein's World of Mathematics, Deficient Number.

FORMULA

A080224(n) + A080225(n) + a(n) = A000005(n).

a(n) = Sum_{d|n} A294934(d) = A294926(n) + A294934(n). - Antti Karttunen, Nov 14 2017

EXAMPLE

All 4 divisors of n=21 are deficient: 1=A005100(1), 3=A005100(3), 7=A005100(6) and 21=A005100(17), therefore a(21)=4.

MATHEMATICA

a[n_] := Sum[If[DivisorSigma[1, d] < 2d, 1, 0], {d, Divisors[n]}];

Array[a, 105] (* Jean-Fran├žois Alcover, Dec 02 2021 *)

PROG

(PARI) A080226(n) = sumdiv(n, d, (sigma(d)<(2*d))); \\ Antti Karttunen, Nov 14 2017

CROSSREFS

Cf. A000203, A005100, A187793, A294926, A294934.

Sequence in context: A135615 A348856 A166469 * A060741 A125747 A060129

Adjacent sequences:  A080223 A080224 A080225 * A080227 A080228 A080229

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 07 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 3 22:23 EDT 2022. Contains 355058 sequences. (Running on oeis4.)