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0, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 3, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 3, 1, 3, 4, 2, 1, 2, 3, 2, 2, 3, 1, 2, 2, 3, 2, 2, 1, 4, 1, 2, 3, 1, 2, 3, 1, 2, 2, 3, 1, 4, 1, 2, 4, 3, 2, 3, 1, 3, 4, 2, 1, 3, 2, 2, 2, 3, 1, 4, 2, 4, 2, 2, 2, 2, 1, 3, 2, 2, 1, 3, 1, 3, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
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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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Table[DigitCount[#, 2, 1] &@ Which[n == 1, 0, MoebiusMu@ n != 0, Total@ Map[#2*2^(PrimePi@ #1 - 1) & @@ # &, FactorInteger[n]], True, With[{r = DivisorSum[n, EulerPhi[#] Abs@ MoebiusMu[#] &]}, SelectFirst[Range[n - 2, 2, -1], DivisorSum[#, EulerPhi[#] Abs@ MoebiusMu[#] &] == r &]]], {n, 105}] (* Michael De Vlieger, Dec 31 2018 *)
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PROG
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(PARI)
A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ From A048675
A285328(n) = { my(r); if((n > 1 && !bitand(n, (n-1))), (n/2), r=A007947(n); if(r==n, 1, n = n-r; while(A007947(n) <> r, n = n-r); n)); };
\\ Or just as:
A322862(n) = if(issquarefree(n), omega(n), hammingweight(A285328(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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