A067543 Numbers k such that phi(k*(k+1)*(k+2)*(k+3)/4!)/phi(k*(k+1)*(k+2)/3!) is not an integer where phi(n) = A000010(n) is the Euler totient function.

6, 8, 16, 24, 40, 46, 54, 56, 64, 78, 80, 104, 118, 126, 128, 136, 144, 160, 176, 198, 203, 208, 224, 240, 248, 280, 304, 328, 344, 358, 360, 376, 414, 416, 440, 464, 486, 488, 496, 520, 526, 544, 560, 568, 584, 616, 630, 640, 656, 680, 688, 726, 736, 784