A340506 For those rows n of A249223 which are weakly increasing, let w(n) denote the maximal entry in the row: sequence gives values of n for which w(n) sets a new record.

1, 6, 72, 120, 1440, 6720, 28800, 80640, 483840, 1612800, 5806080, 7096320, 85155840, 283852800, 510935040, 1476034560, 7947878400, 17712414720, 29520691200, 106274488320, 354248294400, 1653158707200, 2125489766400, 4817776803840, 8029628006400, 28906660823040

Offset

1,2

Comments

This is a companion to A250071 (and is derived from the data for that sequence), which lists the first time k appears as a width.

The record values are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 20, but more data is needed to identify this sequence.

The odd part of a(n) is A053624(n), n>=1. The record values 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 20, ... are the beginning of A053640. - Hartmut F. W. Hoft, Mar 29 2022

Links

Table of n, a(n) for n=1..26.

Formula

a(n) = 2^t(n) * A053624(n), n > 1, where t(n) is the largest exponent satisfying 2^t(n) < A053624(n) and A053624(n) is the odd part of a(n) - see the comment in A250071. - Hartmut F. W. Hoft, Mar 29 2022

Example

a(4) = 120 = 2^3 * A053624(4) = 2^3 * 15 and a(7) = 28800 = 2^7 * A053624(7) = 2^7 * 225. - Hartmut F. W. Hoft, Mar 29 2022

Mathematica

prevPower2[k_] := If[k==1, 1, 2^(Ceiling[Log[2, k]]-1)]
a340506[n_] := Module[{recL={{1, 1}}, q, d, pp}, For[q=1, q<=n, q+=2, d=DivisorSigma[0, q]; pp=prevPower2[q] q; If[First[Last[recL]]<d, AppendTo[recL, {d, pp }]]]; Last[Transpose[recL]]]
a340506[10000000] (* Hartmut F. W. Hoft, Mar 29 2022 *)

Crossrefs

Cf. A237270, A237593, A249223, A250068, A250070, A250071.

Cf. A053624, A053640.

Sequence in context: A242232 A259139 A052615 * A338535 A250071 A192990

Adjacent sequences: A340503 A340504 A340505 * A340507 A340508 A340509

Keyword

nonn,more

Author

N. J. A. Sloane, Jan 23 2021

Extensions

a(12)-a(26) from Hartmut F. W. Hoft, Mar 29 2022

Status

approved