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A332043
Indices of records in A332042.
1
1, 6, 12, 24, 48, 72, 144, 288, 576, 864, 1152, 1440, 1728, 2160, 2304, 2880, 4320, 5760, 8640, 17280, 25920, 34560, 51840, 69120, 103680, 120960, 138240, 155520, 181440, 207360, 241920, 311040, 362880, 414720, 483840, 622080, 725760, 967680, 1244160, 1451520
OFFSET
1,2
COMMENTS
Numbers k such that psi(x) = k has more solutions x than any smaller k, where psi(x) is the Dedekind psi function (A001615).
The corresponding number of solutions for each term is 1, 2, 4, 5, 6, 9, 11, 17, ... (see the link for more values).
EXAMPLE
There are 2 solutions to psi(x) = 6: psi(4) = psi(5) = 6. For all m < 6 there are no more than one solution to psi(x) = m, thus 6 is in the sequence.
MATHEMATICA
psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); m = 10000; v = Table[0, {m}]; Do[i = psi[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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 05 2020
STATUS
approved