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A204831 revision #8

A204831

Numbers n whose divisors can be partitioned into four disjoint sets whose sums are all sigma(n)/4.

27720, 30240, 32760, 50400, 55440, 60480, 65520, 75600, 83160, 85680, 90720, 95760, 98280, 100800, 105840, 110880, 115920, 120120, 120960, 128520, 131040, 138600, 143640, 151200, 163800, 166320, 171360, 180180, 181440, 184800, 191520

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OFFSET

1,1

COMMENTS

Subsequence of A023198 (numbers n such that sigma(n)>=4n).

LINKS

Table of n, a(n) for n=1..31.

EXAMPLE

Number 27720 is in sequence because sigma(27720)/4 = 28080 = 360+27720 = 20+60+280+2310+4620+6930+13860 = 9+30+420+1540+1980+2772+3080+3465+5544+9240 = 1+2+3+4+5+6+7+8+10+11+12+14+15+18+21+22+24+28+33+35+36+40+42+44+45+55+56+63+66+70+72+77+84+88+90+99+105+110+120+126+132+140+154+165+168+180+198+210+220+231+252+264+308+315+330+385+396+440+462+495+504+616+630+660+693+770+792+840+924+990+1155+1260+1320+1386+1848+2520+3960 (summands are all divisors of 27720).

MAPLE

with(numtheory); with(combstruct);

A204831:=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, 4)=0 and 4*n<=s) then

S:=1/4*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:

A204831(100000); # 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), A204830 (numbers n whose divisors can be partitioned into three disjoint sets whose sums are all sigma(n)/3).

Sequence in context: A251235 A023198 A230608 * A345153 A190111 A068404

Adjacent sequences: A204828 A204829 A204830 * A204832 A204833 A204834

KEYWORD

nonn

AUTHOR

Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Jan 22 2012

STATUS

proposed