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

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

Offset: 1

Author

J. Lowell, Jul 08 2019

Keywords

• nonn
• hard
• more

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

Examples

			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).