A134592 -id:A134592 - cp's OEIS frontend

A348568 Highly composite numbers (A002182) such that the exponents of 2 and 3 in their prime factorization are equal.

1, 6, 36, 180, 1260, 7560, 45360, 83160, 498960, 1081080, 6486480, 32432400, 110270160, 551350800, 2095133040, 10475665200, 73329656400, 240940299600, 1686582097200, 48910880818800, 1516237305382800

Offset: 1

Tejo Vrush, Oct 27 2021

These are all the terms in the sequence because for a number x that has exponents of 2 and 3 equal and >= 5 in its prime factorization, 8x/9 is a smaller number with at least the same number of divisors. Since 1516237305382800 is the greatest highly composite number that is not a multiple of 32, A134592(32), it is the last term of this sequence.

			1516237305382800 is highly composite and its prime factorization is 2^4 * 3^4 * 5^2 * 7^2 * 11 * 13 * 17 * 19 * 23 * 29 * 31. Since the exponents of 2 and 3 are both 4, 1516237305382800 is in this sequence.

Cf. A000005, A002182, A064615, A134592.

HCN = Import["https://oeis.org/A002182/b002182.txt", "Table"][[;; , 2]]; Select[HCN, IntegerExponent[#, 2] == IntegerExponent[#, 3] &] (* Amiram Eldar, Oct 27 2021 *)

Intersection of A002182 and A064615.

cp's OEIS Frontend

A348568 Highly composite numbers (A002182) such that the exponents of 2 and 3 in their prime factorization are equal.

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