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A095001
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a(n) = Sum_{d|n} rad(d)^(n/d), where rad(d) = A007947(d) is the squarefree kernel of d.
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2
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1, 3, 4, 7, 6, 24, 8, 23, 31, 68, 12, 196, 14, 192, 384, 279, 18, 1473, 20, 1792, 2552, 2192, 24, 12068, 3131, 8388, 19714, 19124, 30, 116474, 32, 65815, 178512, 131396, 94968, 841093, 38, 524688, 1596560, 1450368, 42, 7280934, 44, 4211500, 16305666
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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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G.f. satisfies: A(x) = Sum_{n>=1} [1/(1-A007947(n)*x^n) - 1].
a(n) = Sum_{d|n} A007947(d)^(n/d); a(p) = p+1, for prime p.
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MATHEMATICA
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rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; a[n_] := DivisorSum[n, rad[#]^(n / #) &]; Array[a, 50] (* Amiram Eldar, Sep 07 2020 *)
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PROG
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(PARI) {a(n)=sumdiv(n, d, prod(i=1, omega(d), factor(d)[i, 1])^(n/d))} /* also formed by the log of G094947(x): */ {a(n)=n*polcoeff(sum(k=1, n, -log(1-prod(i=1, omega(k), factor(k)[i, 1])*x^k+x*O(x^n))/k), 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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