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A344201
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Number of cyclic subgroups of the group (C_n)^n, where C_n is the cyclic group of order n.
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1
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1, 4, 14, 136, 782, 23360, 137258, 4210816, 64576643, 2500000768, 28531167062, 2229573502976, 25239592216022, 1852001137606656, 54736740117685528, 2305878194659557376, 51702516367896047762, 6557734713069408616448, 109912203092239643840222
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{x_1|n, x_2|n, ... , x_n|n} phi(x_1)*phi(x_2)* ... *phi(x_n)/phi(lcm(x_1, x_2, ... , x_n)).
a(n) = Sum_{d|n} b(d, n), where b(n, k) = ( Sum_{d|n} mu(n/d) * d^k )/phi(n).
If p is prime, a(p) = 1 + (p^p - 1)/(p - 1).
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MATHEMATICA
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b[n_, k_] := DivisorSum[n, MoebiusMu[n/#] * #^k &] / EulerPhi[n]; a[n_] := DivisorSum[n, b[#, n] &]; Array[a, 20] (* Amiram Eldar, Oct 04 2023 *)
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PROG
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(PARI) b(n, k) = sumdiv(n, d, moebius(n/d)*d^k)/eulerphi(n);
a(n) = sumdiv(n, d, b(d, n));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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