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A204830 Numbers n whose divisors can be partitioned into three disjoint sets whose sums are all sigma(n)/3. 11
120, 180, 240, 360, 420, 480, 504, 540, 600, 660, 672, 720, 780, 840, 960, 1080, 1260, 1320, 1440, 1512, 1560, 1584, 1620, 1680, 1800, 1848, 1890, 1920, 1980, 2016, 2040, 2160, 2184, 2280, 2340, 2352, 2376, 2400, 2520, 2640, 2688, 2760, 2772, 2856, 2880, 2940, 3000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A023197.

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..500

EXAMPLE

Number 180 is in sequence because sigma(180)/3 = 182 = 2+180 = 1+3+4+5+6+9+10+15+18+30+36+45 = 12+20+60+90 (summands are all divisors of 180).

MAPLE

with(numtheory); with(combstruct);

A204830:=proc(i)

local S, R, Stop, Comb, c, d, k, m, n, s;

for n from 1 to i do

  s:=sigma(n); c:=op(divisors(n));

  if (modp(s, 3)=0 and 3*n<=s) then

     S:=1/3*s-n; R:=select(m->m<=S, [c]); Stop:=false;

     Comb:=iterstructs(Combination(R));

     while not (finished(Comb) or Stop) do

       Stop:=add(d, d=nextstruct(Comb))=S;

     od;

     if Stop then print(n); fi;

  fi;

od;

end:

A204830(1000000); # Paolo P. Lava, Jan 24 2012

CROSSREFS

Cf. A083207 (Zumkeller numbers-numbers n whose divisors can be partitioned into two disjoint sets whose sums are both sigma(n)/2), A204831 (numbers n whose divisors can be partitioned into four disjoint sets whose sums are all sigma(n)/4).

Sequence in context: A090782 A023197 A204828 * A279088 A322377 A247851

Adjacent sequences:  A204827 A204828 A204829 * A204831 A204832 A204833

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Jan 22 2012

STATUS

approved

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Last modified August 13 19:30 EDT 2020. Contains 336451 sequences. (Running on oeis4.)