A335400 Numbers m such that sigma(m)/isigma(m) > sigma(k)/isigma(k) for all k < m, where sigma(m) is the sum of divisors of m (A000203) and isigma(m) is the sum of infinitary divisors of m (A049417).

1, 4, 16, 144, 1296, 3600, 20736, 32400, 176400, 518400, 1587600, 12960000, 25401600, 635040000, 3073593600

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Example

The ratio sigma(m)/isigma(m) for m = 1, 2, 3 and 4 is 1, 1, 1 and 7/5. The record values occur at m = 1 and 4.

Mathematica

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]; f[n_] := DivisorSigma[1, n] / isigma[n]; s={}; fm = 0; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, n]], {n, 1, 2 * 10^5}]; s

Crossrefs

Cf. A000203, A049417, A285906, A335396.

Sequence in context: A335832 A173346 A319166 * A304193 A208661 A334746

Adjacent sequences: A335397 A335398 A335399 * A335401 A335402 A335403

Keyword

nonn,more

Author

Amiram Eldar, Jun 05 2020

Status

approved