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 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) 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

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