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Determine v_2(1)+v_2(2)+...+v_2(n)

Source: Pan African MO 2006 Q4

May 1, 2013
floor functionnumber theory unsolvednumber theory

Problem Statement

For every positive integer kk let a(k)a(k) be the largest integer such that 2a(k)2^{a(k)} divides kk. For every positive integer nn determine a(1)+a(2)+⋯+a(2n)a(1)+a(2)+\cdots+a(2^n).
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