Contribution from Donovan Johnson, Sep 29 2012: (Start)
a(1) = A051278(1) = 4. k/d(k) = 4 for exactly 1 k value: 36.
a(2) = A051279(1) = 1. k/d(k) = 1 for exactly 2 k values: 1 and 2.
a(3) = A051280(1) = 3. k/d(k) = 3 for exactly 3 k values: 9, 18 and 24.
a(4) = A217125(1) = 11264. k/d(k) = 11264 for exactly 4 k values: 360448, 585728, 630784 and 1115136.
a(5) = A217126(1) = 64000. k/d(k) = 64000 for exactly 5 k values: 4096000, 6656000, 7040000, 7168000 and 11520000.
a(6) = A217127(1) = 82944. k/d(k) = 82944 for exactly 6 k values: 7962624, 12939264, 13271040, 13934592, 21565440 and 23224320.
a(7) = 27599616. k/d(k) = 27599616 for exactly 7 k values: 10598252544, 17222160384, 17663754240, 18215746560, 18546941952, 28703600640 and 30911569920. (End)
