Problem Statement

In mathematics, the n-th harmonic number is the sum of the reciprocals of the first n natural numbers: The series of harmonic numbers thus obtained is often loosely referred to as the harmonic series. Harmonic numbers are closely related to the Riemann zeta function, and roughly approximate the natural logarithm function; differing by γ (lowercase Gamma), the Euler–Mascheroni constant. The harmonic series is divergent, albeit quite slowly, and grows toward infinity.

Let's start with the solution:

harmonic(n):=apply("+",1/makelist(i,i,n))$

first_greater_than_n(len):=block(i:1,result:[],while harmonic(i)<=len do (result:endcons(i,result),i:i+1),last(result)+1)$

/* Test cases */
/* First 20 harmonic numbers */
makelist(harmonic(j),j,20);

/* First harmonic number that exceeds a positive integer from 1 to 5 */
makelist(first_greater_than_n(k),k,5);