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

Author

N. J. A. Sloane, Jan 23 2021

Keywords

• nonn
• more

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

Examples

			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
		

Crossrefs

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

Cf. A053624, A053640.

Programs

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]]Hartmut F. W. Hoft, Mar 29 2022 *)

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

Extensions

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