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A347428
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Expansion of g.f. Product_{k>=2} 1/(1-x^phi(k)).
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1
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1, 1, 4, 4, 14, 14, 40, 40, 106, 106, 254, 254, 582, 582, 1256, 1256, 2620, 2620, 5256, 5256, 10266, 10266, 19482, 19482, 36204, 36204, 65792, 65792, 117496, 117496, 206120, 206120, 356320, 356320, 606912, 606912, 1020848, 1020848, 1695676, 1695676, 2786010
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OFFSET
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0,3
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LINKS
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David P. Roberts and Fernando Rodriguez Villegas, Hypergeometric Motives, arXiv:2109.00027 [math.AG], 2021. See (5.2) p. 6.
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FORMULA
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log(a(n)) ~ sqrt(105*zeta(3)*n)/Pi. (End)
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MAPLE
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with(numtheory):
b:= proc(n) option remember; nops(invphi(n)) end:
g:= proc(n) option remember; `if`(n=0, 1, add(
g(n-j)*add(d*b(d), d=divisors(j)), j=1..n)/n)
end:
a:= n-> g(n)-g(n-1):
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MATHEMATICA
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nt = 100; (* number of terms *)
f[kmax_] := f[kmax] = CoefficientList[Product[1/(1 - x^EulerPhi[k]), {k, 2, kmax}] + O[x]^nt, x]; f[kmax = nt]; f[kmax += nt];
While[f[kmax] != f[kmax - nt], kmax += nt];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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