product of all multiplicative functions
n = 1 ∑ ∞ n 1 7 2 9 ϕ μ τ σ λ e ( n ) = b π a a + b = ? notations
all functions are listed in this wiki
The answer is 1.
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1 solution
Thanks, i have edited the problem.
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Wait what?
Comrade @Aareyan Manzoor : I have a question on your recent roots of unity problem... you know I love those ;) Comparing the derivatives, I'm finding that the RHS is n L i 2 ( x n ) . Am I on the right track? Maybe a calculus error?
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I am sorry; i made an error. I had initially thought of n-1 but ended up writing n in the upper limit of the boundary of the summation.
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@Aareyan Manzoor – yes, that's what I thought... so you get a coefficient -1 on the other side. great problem though!
Not as bad as it looks!
Since e ( 1 ) = 1 and e ( n ) = 0 for n > 1 , the sum is 1 = 1 π 0 , and the answer is 1 .
PS: You should tell us to enter a + b as the answer! I assumed...