A centered octagonal number is a centeredfigurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.[1] The centered octagonal numbers are the same as the oddsquare numbers.[2] Thus, the nth centered octagonal number is given by the formula
Calculating Ramanujan's tau function on a centered octagonal number yields an odd number, whereas for any other number the function yields an even number.[2]
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