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A332039
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Indices of records in A332038.
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4
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1, 12, 24, 60, 120, 240, 360, 720, 1440, 2880, 4320, 5760, 7200, 8640, 11520, 14400, 17280, 21600, 25920, 28800, 34560, 43200, 60480, 86400, 120960, 129600, 172800, 241920, 259200, 302400, 345600, 483840, 518400, 604800, 907200, 1036800, 1209600, 1814400, 2419200
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OFFSET
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1,2
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COMMENTS
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Numbers k such that isigma(x) = k has more solutions x than any smaller k, where isigma(x) is the sum of infinitary divisors of x (A049417).
The corresponding number of solutions for each term is 1, 2, 3, 5, 7, 12, 13, 20, ... (see the link for more values).
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LINKS
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EXAMPLE
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There are 3 solutions to isigma(x) = 24: isigma(14) = isigma(15) = isigma(23) = 24. For all m < 24 there are 2 or fewer solutions to isigma(x) = m, thus 24 is in the sequence.
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MATHEMATICA
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fun[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ (fun @@@ FactorInteger[n]); m = 10000; v = Table[0, {m}]; Do[i = isigma[k]; If[i <= m, v[[i]]++], {k, 1, m}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 1, m}]; s
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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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