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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A083209 Numbers with exactly one subset of their sets of divisors such that the complement has the same sum. 13
6, 12, 20, 28, 56, 70, 88, 104, 176, 208, 272, 304, 368, 464, 496, 550, 650, 736, 836, 928, 992, 1184, 1312, 1376, 1504, 1696, 1888, 1952, 2752, 3008, 3230, 3392, 3770, 3776, 3904, 4030, 4288, 4510, 4544, 4672, 5056, 5170, 5312, 5696, 5830, 6208, 6464 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A083206(a(n))=1; perfect numbers (A000396) are a subset; problem: are weird numbers (A006037) a subset?

The weird numbers A006037 are not a subset of this sequence. The first missing weird number is A006037(8) = 10430. - Alois P. Heinz, Oct 29 2009

All numbers of the form p*2^k are in this sequence for k>0 and odd primes p between 2^(k+1)/3 and 2^(k+1). - T. D. Noe, Jul 08 2010

LINKS

T. D. Noe, Table of n, a(n) for n=1..407 (terms < 10^6)

Eric Weisstein's World of Mathematics, Perfect Number.

Eric Weisstein's World of Mathematics, Weird Number.

Reinhard Zumkeller, Illustration of initial terms

EXAMPLE

n=20: 2+4+5+10 = 1+20, 20 is a term (A083206(20)=1).

MAPLE

with(numtheory): b:= proc(n, l) option remember; local m, ll, i; m:= nops(l); if n<0 then 0 elif n=0 then 1 elif m=0 or add(i, i=l)<n then 0 else ll:= subsop(m=NULL, l); b(n, ll) +b(n-l[m], ll) fi end: a:= proc(n) option remember; local i, k, l, m, r; for k from `if`(n=1, 1, a(n-1)+1) do l:= sort([divisors(k)[]]); m:= iquo(add(i, i=l), 2, 'r'); if r=0 and b(m, l)=2 then break fi od; k end: seq(a(n), n=1..30); # Alois P. Heinz, Oct 29 2009

MATHEMATICA

b[n_, l_] := b[n, l] = Module[{m, ll, i}, m = Length[l]; Which[n<0, 0, n == 0, 1, m == 0 || Total[l]<n, 0, True, ll = ReplacePart[l, m -> Nothing]; b[n, ll] + b[n - l[[m]], ll]]]; a[n_] := a[n] = Module[{i, k, l, m, r}, For[k = If[n == 1, 1, a[n-1]+1], True, k++, l = Divisors[k]; {m, r} = QuotientRemainder[Total[l], 2]; If[r==0 && b[m, l]==2, Break[]]]; k]; Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 50}] (* Jean-François Alcover, Jan 31 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A005101, A005835, A064771.

Sequence in context: A356141 A079760 A109895 * A339858 A080714 A116368

Adjacent sequences: A083206 A083207 A083208 * A083210 A083211 A083212

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Apr 22 2003

EXTENSIONS

More terms from Alois P. Heinz, Oct 29 2009

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 December 5 06:35 EST 2022. Contains 358582 sequences. (Running on oeis4.)