%I #9 Apr 21 2020 21:35:15

%S 30,40,80,84,126,160,180,200,210,252,270,280,288,306,320,330,360,400,

%T 420,440,450,462,468,480,520,540,546,560,576,588,594,600,612,630,640,

%U 648,660,680,704,728,756,760,780,792,800,864,880,882,900,920,924,972

%N Sums of two numbers such that neither of their number of divisors divides n but the number of divisors of their product and difference do.

%e 30 is in the sequence since 30 = 6 + 24; neither d(6) = 4 nor d(24) = 8 divide 30, but d(6*24) = d(144) = 15 | 30 and d(24-6) = d(18) = 6 | 30.

%t Flatten[Table[If[Sum[(1 - Ceiling[n/DivisorSigma[0, i (n - i)]] + Floor[n/DivisorSigma[0, i (n - i)]]) (1 - Ceiling[n/DivisorSigma[0, n - 2 i]] + Floor[n/DivisorSigma[0, n - 2 i]]) (Ceiling[n/DivisorSigma[0, i]] - Floor[n/DivisorSigma[0, i]]) (Ceiling[n/DivisorSigma[0, n - i]] - Floor[n/DivisorSigma[0, n - i]]), {i, Floor[(n - 1)/2]}] > 0, n, {}], {n, 1000}]]

%Y Cf. A033950.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Jul 21 2019

%E Name corrected by _Wesley Ivan Hurt_, Jul 24 2019