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A190117
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a(n) = Sum_{k=1..n} k*k', where n' is the arithmetic derivative of n.
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1
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0, 2, 5, 21, 26, 56, 63, 159, 213, 283, 294, 486, 499, 625, 745, 1257, 1274, 1652, 1671, 2151, 2361, 2647, 2670, 3726, 3976, 4366, 5095, 5991, 6020, 6950, 6981, 9541, 10003, 10649, 11069, 13229, 13266, 14064, 14688, 17408, 17449, 19171, 19214, 21326, 23081, 24231, 24278, 29654, 30340, 32590
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OFFSET
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1,2
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LINKS
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EXAMPLE
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1*1'+2*2'+3*3'=0+2+3=5 ->a(3)= 5.
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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(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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