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A332041
Indices of records in A332040.
2
1, 6, 30, 330, 390, 2730, 5460, 12090, 60060, 92820, 223860, 1021020, 1922700, 3805620, 13458900, 41861820, 110362980, 113573460, 227146920, 251170920, 502341840, 563603040, 888287400, 1270629360, 1776574800, 3310889400, 23107724640, 27939071160, 33754921200, 36419783400
OFFSET
1,2
COMMENTS
Numbers k such that esigma(x) = k has more solutions x than any smaller k, where esigma(x) is the sum of exponential divisors of x (A051377).
The exponential version of A145899.
The corresponding number of solutions for each term is 1, 2, 5, 6, 8, 9, 10, 12, 15, 16, 19, 22, 27, 29, 35, 37, 38, 44, 45, 47, 50, 51, 52, 53, 66, 80, 83, 89, 95, 102.
EXAMPLE
There are 2 solutions to esigma(x) = 6: esigma(4) = esigma(6) = 6. For all m < 6 there are no more than one solution to esigma(x) = m, thus 6 is in the sequence.
MATHEMATICA
f[p_, e_] := DivisorSum[e, p^# &]; esigma[1] = 1; esigma[n_] := Times @@ f @@@ FactorInteger[n]; m = 10000; v = Table[0, {m}]; Do[sig = esigma[k]; If[sig <= m, v[[sig]]++], {k, 1, m}]; s = {}; vm = -1; Do[If[v[[k]] > vm, vm = v[[k]]; AppendTo[s, k]], {k, 1, m}]; s
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 05 2020
EXTENSIONS
a(26)-a(30) from Giovanni Resta, Feb 06 2020
STATUS
approved