What are the next two numbers in this sequence?
1, 2, 3, 5, 6, 9, 10, 15, 18, 24, 25, 34, 35, ??, ??

(In reply to

answer by K Sengupta)

Let S(p) denote the pth term of the given sequence.

Then, we observe that the terms of the given sequence are in conformity wih the following recurrence relationship:

S(p) = S(p-1) + S(T(p)), where T(x) denotes the largest divisor of x (excluding x).

Thus,

S(1) + S(T(2)) = 1 + S(2) = 1+ 1 = 2 = S(2)

S(2) + S(T(3) = 2 + S(3) = 2 + 1 = 3 = S(3)

S(3) + S(T(4)) = 3 + S(2) = 3 + 2 = 5 = S(4)

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S(14) = S(13) + S(T(14)) = 35 + S(7) = 35 + 10 = 45

S(15) = S(14) + S(T(15)) = 45 + S(5) = 45 + 6 = 51

Consequently, the required next two numbers in the given sequence are 45 and 51.