A376156 - OEIS

%I #4 Sep 13 2024 08:07:25

%S 2,5,23,83,536,2519,45359,16736,743398,1908958,3386606,9295535

%N a(n) is the least number that is the sum of the nonprime divisors of k for exactly n different k.

%e 2 is not the sum of the nonprime divisors of any k.

%e 5 is the sum of the nonprime divisors of 4 (1 + 4 = 5).

%e 23 is the sum of the nonprime divisors of 12 (1 + 4 + 6 + 12) and of 22 (1 + 22).

%e 83 is the sum of the nonprime divisors of 40 (1 + 4 + 8 + 10 + 20 + 40) and 52 (1 + 4 + 26 + 52) and 82 (1 + 82).

%p N:= 10^6: # for terms < 10^6

%p f:= proc(n) convert(remove(isprime, numtheory:-divisors(n)),`+`) end proc:

%p R:= Vector(N):

%p for i from 1 to N do

%p   v:= f(i);

%p   if v <= N then R[v]:= R[v]+1 fi

%p od:

%p m:= convert(R,set)[-2]:

%p V:= Array(0..m): count:= 0:

%p for i from 2 while count < m+1 do

%p if V[R[i]] = 0 then V[R[i]]:= i; count:= count+1 fi

%p od:

%p convert(V,list);

%Y Cf. A023890.

%K nonn,more

%O 0,1

%A _Robert Israel_, Sep 12 2024