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

Author

Daniel Lignon, Dec 30 2019

Keywords

• nonn
• base

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

Examples

			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.
		

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).

Crossrefs

Cf. A066044, A279930, A284758, A309039, A309493, A371812.