A272605 -id:A272605 - cp's OEIS frontend

A319865 Product of distinct prime factors of highly composite numbers (definition 1, A002182).

1, 2, 2, 6, 6, 6, 6, 6, 30, 30, 30, 30, 30, 30, 210, 210, 210, 210, 210, 210, 210, 210, 210, 210, 2310, 210, 210, 2310, 2310, 2310, 2310, 2310, 2310, 2310, 2310, 2310, 2310, 30030, 30030, 30030, 30030, 30030, 30030, 30030, 30030, 30030, 30030, 30030, 30030, 30030, 30030, 30030, 510510, 30030

Offset: 1

Seiichi Manyama, Sep 29 2018

nonn

			n  | A002182(n)                       | a(n)
---+----------------------------------+--------------------------
24 | 25200 = 2^4 * 3^2 * 5^2 * 7      |  210 = 2 * 3 * 5 * 7
25 | 27720 = 2^3 * 3^2 * 5   * 7 * 11 | 2310 = 2 * 3 * 5 * 7 * 11
26 | 45360 = 2^4 * 3^4 * 5   * 7      |  210 = 2 * 3 * 5 * 7
27 | 50400 = 2^5 * 3^2 * 5^2 * 7      |  210 = 2 * 3 * 5 * 7

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Highly Composite Number
Wikipedia, Highly composite number

Cf. A002182, A007947, A108602, A112779, A272605.

a(n) = A007947(A002182(n)). - Michel Marcus, Sep 30 2018

A352699 Highly composite numbers that cease to be highly composite if divided by their largest prime factor.

Original entry on oeis.org

24, 48, 360, 720, 7560, 10080, 15120, 20160, 25200, 45360, 50400, 332640, 665280, 10810800, 14414400, 17297280, 21621600, 32432400, 43243200, 1102701600, 2205403200, 27935107200, 48886437600, 73329656400, 97772875200, 146659312800, 293318625600, 1606268664000

Offset: 1

J. Lowell, Mar 30 2022

nonn

			24 itself is highly composite, but the largest prime factor of 24 is 3, and 24/3 = 8, which is not highly composite. So 24 is a term of this sequence.

Amiram Eldar, Table of n, a(n) for n = 1..1199

Cf. A002182, A006530, A052126, A272605.

With[{hcn = Cases[Import["https://oeis.org/A002182/b002182.txt", "Table"], {, }][[;; , 2]]}, Select[hcn, FreeQ[hcn, #/FactorInteger[#][[-1, 1]]] &, 28]] (* Amiram Eldar, Mar 13 2023 *)

cp's OEIS Frontend

A319865 Product of distinct prime factors of highly composite numbers (definition 1, A002182).

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