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A185283
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Least k such that sigma(1) + sigma(2) + sigma(3) +...+ sigma(k) >= n.
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6
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0, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10
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OFFSET
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0,3
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LINKS
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EXAMPLE
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a(3) = 2 because sigma(1) + sigma(2) + sigma(3) = 1+3+4 > 3.
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MAPLE
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b:= proc(n) option remember; `if`(n=0, 0,
numtheory[sigma](n)+b(n-1))
end:
a:= proc(n) option remember; local k; for k from
`if`(n=0, 0, a(n-1)) do if b(k)>=n then return k fi od
end:
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MATHEMATICA
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a[n_] := (k = 1; While[ Total[ DivisorSigma[1, Range[k]]] < n, k++]; k); Table[ a[n], {n, 1, 90}]
Module[{nn=10, ad, th}, ad={#[[1]], #[[2]]}&/@Partition[Accumulate[ DivisorSigma[ 1, Range[nn]]], 2, 1]; th=Thread[{Range[2, nn], ad}]; Join[ {0, 1}, Flatten[Table[#[[1]], #[[2, 2]]-#[[2, 1]]]&/@th]]] (* Harvey P. Dale, Aug 29 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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