A332041 Indices of records in A332040.

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.

Links

Table of n, a(n) for n=1..30.

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

Cf. A051377, A145899, A289132, A332037, A332039, A332040.

Sequence in context: A360831 A232978 A359882 * A201135 A369135 A111876

Adjacent sequences: A332038 A332039 A332040 * A332042 A332043 A332044

Keyword

nonn

Author

Amiram Eldar, Feb 05 2020

Extensions

a(26)-a(30) from Giovanni Resta, Feb 06 2020

Status

approved