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A348976
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Möbius transform of A129283, which is sum of n and its arithmetic derivative.
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5
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1, 2, 3, 5, 5, 5, 7, 12, 11, 9, 11, 12, 13, 13, 14, 28, 17, 17, 19, 22, 20, 21, 23, 28, 29, 25, 39, 32, 29, 22, 31, 64, 32, 33, 34, 40, 37, 37, 38, 52, 41, 32, 43, 52, 50, 45, 47, 64, 55, 49, 50, 62, 53, 57, 54, 76, 56, 57, 59, 52, 61, 61, 72, 144, 64, 52, 67, 82, 68, 58, 71, 92, 73, 73, 78, 92, 76, 62, 79, 120
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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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MATHEMATICA
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f[p_, e_] := e/p; d[1] = 1; d[n_] := n*(1 + Plus @@ f @@@ FactorInteger[n]); a[n_] := DivisorSum[n, MoebiusMu[#]*d[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 13 2021 *)
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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]));
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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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