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A347428 Expansion of g.f. Product_{k>=2} 1/(1-x^phi(k)). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
David P. Roberts and Fernando Rodriguez Villegas, Hypergeometric Motives, arXiv:2109.00027 [math.AG], 2021. See (5.2) p. 6.
FORMULA
From Vaclav Kotesovec, Sep 02 2021: (Start)
For n>0, a(n) = A120963(n) - A120963(n-1).
log(a(n)) ~ sqrt(105*zeta(3)*n)/Pi. (End)
MAPLE
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):
seq(a(n), n=0..40); # Alois P. Heinz, Jun 23 2023
MATHEMATICA
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];
f[kmax] (* Jean-François Alcover, Nov 29 2023 *)
CROSSREFS
Cf. A000010 (phi), A014197, A051894, A120963 (similar g.f.).
Sequence in context: A097335 A255297 A339319 * A361801 A263870 A263796
KEYWORD
nonn
AUTHOR
Michel Marcus, Sep 02 2021
EXTENSIONS
Terms a(16) and beyond corrected by Vaclav Kotesovec, Jun 23 2023, following a suggestion from Georg Fischer
STATUS
approved

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Last modified March 1 12:07 EST 2024. Contains 370433 sequences. (Running on oeis4.)