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A190118
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a(n) = Sum_{k=1..n} k/gcd(k,k'), where n' is arithmetic derivative of n.
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3
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1, 3, 6, 7, 12, 18, 25, 27, 30, 40, 51, 54, 67, 81, 96, 97, 114, 120, 139, 144, 165, 187, 210, 216, 221, 247, 248, 255, 284, 314, 345, 347, 380, 414, 449, 452, 489, 527, 566, 576, 617, 659, 702, 713, 728, 774, 821, 824, 831, 841
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OFFSET
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1,2
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COMMENTS
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Use gcd(1,0)=1.
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LINKS
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EXAMPLE
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1/gcd(1,1')+2/gcd(2,2')+3/gcd(3,3')=1+2/1+3/1=6 ->a(3)=6.
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MAPLE
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der:=n->n*add(op(2, p)/op(1, p), p=ifactors(n)[2]):
seq(add(i/gcd(der(i), i), i=1..n), n=1..50);
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MATHEMATICA
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A003415[n_]:= If[Abs@n < 2, 0, n Total[#2/#1 & @@@FactorInteger[Abs@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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