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A308667
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(1/n) times the number of n-member subsets of [n^2] whose elements sum to a multiple of n.
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3
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1, 1, 10, 115, 2126, 54086, 1753074, 69159399, 3220837534, 173103073384, 10551652603526, 719578430425845, 54297978110913252, 4492502634538340722, 404469190271900056316, 39370123445405248353743, 4120204305690280446004838, 461365717080848755611811094
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OFFSET
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1,3
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LINKS
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FORMULA
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a(p) == 1 (mod p^3) for all primes p >= 5 (apply Meštrović, Remark 17, p. 12). - Peter Bala, Mar 28 2023
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MAPLE
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with(numtheory):
a:= proc(n) option remember; add(phi(n/d)*
(-1)^(n+d)*binomial(n*d, d), d=divisors(n))/n^2
end:
seq(a(n), n=1..20);
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MATHEMATICA
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a[n_] := a[n] = Sum[EulerPhi[n/d]*
(-1)^(n + d)*Binomial[n*d, d], {d, Divisors[n]}]/n^2;
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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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