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A258171
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a(n) = Sum_{d|n} phi(d)*Bell(n/d) for n>0, a(0) = 0.
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3
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0, 1, 3, 7, 19, 56, 214, 883, 4163, 21163, 116039, 678580, 4213848, 27644449, 190900217, 1382958677, 10480146333, 82864869820, 682076827740, 5832742205075, 51724158351527, 474869816158547, 4506715739125923, 44152005855084368, 445958869299027638
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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MAPLE
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with(numtheory):
A:= proc(n, k) option remember;
add(phi(d)*k^(n/d), d=divisors(n))
end:
T:= (n, k)-> add((-1)^(k-i)*binomial(k, i)*A(n, i), i=0..k)/k!:
a:= n-> add(T(n, k), k=0..n):
seq(a(n), n=0..30);
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MATHEMATICA
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a[n_] := If[n == 0, 0, DivisorSum[n, EulerPhi[#] BellB[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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EXTENSIONS
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STATUS
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approved
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