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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.
5
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
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 *)
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