Complex Devaraj numbers
 

Recall that if N = p_1*p_2....p_r and if ((P_1-1)*(N-1)^(r-2)/((p_2-1)… (p_r-1)) is an integer then N is a Devaraj number. Q: are there complex Devaraj numbers? Yes here is an example: N = (2 - I)*((3 + 2*I)*(4-I)= 33 - 4*I is a Devaraj number since

((1-I)*(32 -4*I)/(2+3*I)*(3-I)) = 1 -5*I, a Gaussian integer.

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