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

1,2

Comments

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.

Links

Table of n, a(n) for n=1..21.

Formula

Intersection of A002182 and A064615.

Example

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.

Mathematica

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

Crossrefs

Cf. A000005, A002182, A064615, A134592.

Sequence in context: A258629 A294465 A074444 * A366630 A209904 A146883

Adjacent sequences: A348565 A348566 A348567 * A348569 A348570 A348571

Keyword

nonn,fini,full

Author

Tejo Vrush, Oct 27 2021

Status

approved