A131902 - OEIS

%I #4 Mar 30 2018 03:05:35

%S 6,14,10,14,16,20,21,33,24,28,20,30,33,30,34,30,54,40,24,42,44,42,66,

%T 30,48,42,60,57,68,44,54,40,60,66,54,52,63,85,102,74,66,104,88,66,80,

%U 60,84,99,93,96,86,114,76,132,105,102,60,88,111,90,138,105,114,102,105,138,96

%N Smallest positive integer k with the same sum of divisors as the n-th integer for which such a k exists.

%H Robert Israel, <a href="/A131902/b131902.txt">Table of n, a(n) for n = 1..10000</a>

%F Let S={n>0 : there exists a k>0 and k<n with sigma(k)=sigma(n)}. Then a(n):=min(k>0: sigma(k)=sigma(n-th element of S)

%e a(3)=10 because 17 is the third integer for which a smaller integer with same sum of divisors exists and sigma(17)=1+17=18 and sigma(10)=1+2+5+10=18 and there is no k>0 less than 10 with sigma(k)=18

%p N:= 1000: # to use values of sigma <= N

%p V:= Vector(N): A:= Vector(N):

%p for n from 1 to N do

%p   v:= numtheory:-sigma(n);

%p   if v <= N then

%p     if V[v] = 0 then V[v]:= n

%p     else A[n]:= V[v]

%p     fi

%p   fi

%p od:

%p subs(0=NULL, convert(A,list)); # _Robert Israel_, Mar 30 2018

%t Clear[tmp]; Function[n,If[Head[ #1]===tmp,#1=n;Unevaluated[Sequence[]],#1]& [tmp[DivisorSigma[1,n]]]]/@Range[200]

%Y Cf. A069822, A131903 - A131908.

%K easy,nonn

%O 1,1

%A Peter Pein (petsie(AT)dordos.net), Jul 26 2007