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Thursday, October 31, 2019

Entry 55

Define dk=η(kτ) with Dedekind eta function η(τ). Then for Level 60,
d2d3d5d12d20d30d1d4d6d10d15d60+1=(d2d3d5d12d20d30)(d2d30)3(d1d4d6d10d15d60)2d2d3d5d12d20d30d1d4d6d10d15d601=(d6d10)3d2d3d5d12d20d30
Or more simply a+1=ba1=c we find (a,b,c) as the McKay-Thompson series of class 60C for Monster (A145725). They obey,
(4abc+bca)+2a=abc+bca+acb
If we express a=pq as
p=d2d3d5d12d20d30q=d1d4d6d10d15d60
then we have the simple cube,pq+q2p=(d2d30)3 where, of course, Level 60=2×30.

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