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A351573
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Arithmetic derivative of the largest unitary divisor of n that is an exponentially odd number.
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3
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0, 1, 1, 0, 1, 5, 1, 12, 0, 7, 1, 1, 1, 9, 8, 0, 1, 1, 1, 1, 10, 13, 1, 44, 0, 15, 27, 1, 1, 31, 1, 80, 14, 19, 12, 0, 1, 21, 16, 68, 1, 41, 1, 1, 1, 25, 1, 1, 0, 1, 20, 1, 1, 81, 16, 92, 22, 31, 1, 8, 1, 33, 1, 0, 18, 61, 1, 1, 26, 59, 1, 12, 1, 39, 1, 1, 18, 71, 1, 1, 0, 43, 1, 10, 22, 45, 32, 140, 1, 7, 20, 1, 34
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OFFSET
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1,6
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LINKS
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FORMULA
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MATHEMATICA
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f1[p_, e_] := If[OddQ[e], p^e, 1]; f2[p_, e_] := If[OddQ[e], e/p, 0]; a[1] = 0; a[n_] := (Times @@ f1 @@@ (f = FactorInteger[n])) * (Plus @@ f2 @@@ f); Array[a, 100] (* Amiram Eldar, Feb 23 2022 *)
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PROG
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(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A350389(n) = { my(m=1, f=factor(n)); for(k=1, #f~, if(1==(f[k, 2]%2), m *= (f[k, 1]^f[k, 2]))); (m); };
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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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