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A206447
Composite numbers n such that sigma(n) = sigma(d) has solution for some other composite number d.
2
14, 15, 16, 20, 24, 25, 26, 28, 30, 33, 35, 38, 39, 40, 42, 44, 46, 48, 51, 54, 55, 56, 58, 60, 62, 65, 66, 68, 69, 70, 75, 77, 78, 80, 82, 84, 87, 88, 90, 92, 94, 95, 96, 99, 102, 104, 105, 108, 110, 112, 114, 115, 116, 118, 119, 120, 122, 123, 124, 125
OFFSET
1,1
LINKS
EXAMPLE
Composite numbers 14 and 15 are in sequence because sigma(14) = sigma(15) = 24.
MAPLE
N:= 500:
Res:= {}: Q:= {}:
for n from 4 to N do
if isprime(n) then next fi;
s:= numtheory:-sigma(n);
if not assigned(V[s]) then
V[s]:= n;
if s > N then Q:= Q union {n} fi;
else
Res:= Res union {n, V[s]};
if s > N then Q:= Q minus {V[s]} fi;
fi
od:
convert(select(`<`, Res, min(Q)), list); # Robert Israel, Dec 17 2017
MATHEMATICA
t2 = Table[If[PrimeQ[n], 0, DivisorSigma[1, n]], {n, 1000}]; Select[Range[132], ! PrimeQ[#] && Length[Position[t2, t2[[#]]]] > 1 &] (* T. D. Noe, Feb 27 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Feb 07 2012
STATUS
approved