%I #12 Feb 01 2022 15:55:44
%S 2,3,4,5,6,7,8,9,12,13,14,15,16,17,18,20,21,24,26,27,28,29,30,31,32,
%T 33,36,37,38,41,42,43,44,45,47,48,49,50,54,56,57,58,59,60,62,65,68,70,
%U 71,72,73,76,77,79,80,81,82,84,85,86,90,91,92,93,98,100,105,106,107,108
%N Numbers that are the sum of two balanced numbers in at least one way.
%C A balanced number k is a number such that phi(k) | sigma(k).
%e 8 is in the sequence since the balanced numbers less than 8 are: 1, 2, 3, 6 and 6 + 2 = 8.
%e 10 is not in the sequence since the balanced numbers less than 10 are: 1, 2, 3, 6, and no two sum to 10.
%t m = 100; balanced = Select[Range[m], Divisible[DivisorSigma[1, #], EulerPhi[#]] &]; q[n_] := Length[IntegerPartitions[n, {2}, balanced]] > 0; Select[Range[m], q] (* _Amiram Eldar_, Feb 01 2022 *)
%o (PARI) isb(n) = (sigma(n) % eulerphi(n)) == 0;
%o isok(m) = for (k=1, m-1, if (isb(k) && isb(m-k), return(1))); \\ _Michel Marcus_, Feb 01 2022
%Y Cf. A020492 (balanced numbers).
%K nonn
%O 1,1
%A _Wesley Ivan Hurt_, Feb 01 2022