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

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..7.

Example

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

Crossrefs

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

Sequence in context: A353899 A308618 A283021 * A087902 A282193 A180213

Adjacent sequences: A309036 A309037 A309038 * A309040 A309041 A309042

Keyword

nonn,hard,more

Author

J. Lowell, Jul 08 2019

Status

approved