A309493 -id:A309493 - cp's OEIS frontend

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

Daniel Lignon, Dec 30 2019

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

			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.

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

Bernard Schott, Table of n, a(n) for n = 1..91.
Wikipédia, Nombre brésilien (last paragraph).

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

A309039 Highly composite numbers (A002182) that are not highly Brazilian (A329383).

Original entry on oeis.org

2, 4, 6, 12, 36, 48, 240

Offset: 1

J. Lowell, Jul 08 2019

Is there a proof that this sequence is infinite?

Indeed, from 1680 to 2882880, that is, during 26 successive terms (maybe more?), highly composite numbers are the same as highly Brazilian numbers. - Bernard Schott, Jul 12 2019

			2 is a highly composite number (A002182) but is not in A329383 (where 1 is followed immediately by 7), so 2 is a term of this sequence.
48 is highly composite with tau(48) = 10, and 48 = 66_7 = 44_11 = 33_15 = 22_33 so beta(48) = 4. We have also beta(40) = 4 with 40 = 1111_3 = 55_7 = 44_9 = 22_19 so 48 is not highly Brazilian. 48 is a term because it is highly composite but not highly Brazilian. - _Bernard Schott_, Jul 12 2019

Cf. A002182 (highly composites), A329383 (highly Brazilian numbers), A279930 (highly composites and highly Brazilian numbers), A309493 (highly Brazilian numbers not highly composites).

cp's OEIS Frontend

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

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