A206447 Composite numbers n such that sigma(n) = sigma(d) has solution for some other composite number d.

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

Author

Jaroslav Krizek, Feb 07 2012

Keywords

• nonn

Examples

			Composite numbers 14 and 15 are in sequence because sigma(14) = sigma(15) = 24.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A206036, A158913, A066073.

Programs

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 *)