A329383 Positive integers that have more Brazilian representations than any smaller positive integer.

1, 7, 15, 24, 40, 60, 120, 180, 336, 360, 720, 840, 1260, 1440, 1680, 2520, 5040, 7560, 10080, 15120, 20160, 25200, 27720, 45360, 50400, 55440, 83160, 110880, 166320, 221760, 277200, 332640, 498960, 554400, 665280, 720720, 1081080, 1441440, 2162160, 2882880

Offset

1,2

Comments

By analogy with highly composite numbers (A002182), these numbers could be called highly Brazilian numbers.

Also, records in A284758.

The representation n = 11_(n-1) is allowed in A066044, but it is not allowed for Brazilian numbers. Hence 3 = 11_2 = A066044(2) is not Brazilian and therefore not highly Brazilian. However, except for 3, the sequences A066044 and this one are the same.

The first time the name "highly Brazilian number" was used is in Daniel Lignon's book in reference. - Bernard Schott, Jul 27 2020

References

D. Lignon, Dictionnaire de (presque) tous les nombres entiers, Editions Ellipses, 2012, see p. 420. [In French.]

Links

Bernard Schott, Table of n, a(n) for n = 1..91.

Wikipédia, Nombre brésilien (last paragraph).

Example

40 is a term since 40 = 1111_3 = 55_7 = 44_9 = 22_19 and it's the smallest number with 4 representations as a Brazilian number.

Crossrefs

Cf. A066044, A279930, A284758, A309039, A309493.

Sequence in context: A184920 A076796 A056119 * A284758 A334798 A211430

Adjacent sequences: A329380 A329381 A329382 * A329384 A329385 A329386

Keyword

nonn,base

Author

Daniel Lignon, Dec 30 2019

Status

approved