cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A372849 Number of pairs of two disjoint sets of n positive integers more than 1 with product A354697.

Original entry on oeis.org

1, 4, 2, 25, 7, 31, 55, 114, 237, 695, 1666, 2646, 6928, 42986, 79098, 126721, 375348, 667321, 1831927, 7130833, 12067929, 42973699, 105786888, 218943019, 646950177, 1476274502, 3846678717, 14320262729, 46445678648, 91771247330, 182567269925
Offset: 2

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Author

Zhao Hui Du, May 14 2024

Keywords

Crossrefs

Cf. A354697.

A354457 a(n) is the least integer for which there exist two disjoint sets of n positive integers each, all distinct, for which the product of the integers in either set is a(n).

Original entry on oeis.org

6, 36, 240, 2520, 30240, 443520, 6652800, 133056000, 2075673600, 58118860800, 1270312243200, 29640619008000, 844757641728000, 25342729251840000, 810967336058880000, 27978373094031360000, 1077167364120207360000, 43086694564808294400000, 1499416970855328645120000
Offset: 2

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Author

Andy Niedermaier, May 30 2022

Keywords

Comments

This is also the least integer that can be represented as the product of the integers > 1 in two disjoint sets, one having n terms and the other having n-1 terms.
From Jon E. Schoenfield, May 12 2024: (Start)
For n >= 2, let b(n) be the square root of the smallest square that can be expressed as the product of 2*n distinct positive integers; then a(n) >= b(n).
Conjecture: for every n >= 2, a(n) = b(n). (End)

Examples

			From _Jinyuan Wang_, May 31 2022: (Start)
For n=2,       6 = 1*6                  = 2 * 3.
For n=3,      36 = 1*4*9                = 2 * 3 * 6.
For n=4,     240 = 1*3*8*10             = 2 * 4 * 5 * 6.
For n=5,    2520 = 1*2*9*10*14          = 3 * 4 * 5 * 6 * 7.
For n=6,   30240 = 1*2*6*10*14*18       = 3 * 4 * 5 * 7 * 8 * 9.
For n=7,  443520 = 1*2*5*9*14*16*22     = 3 * 4 * 6 * 7 * 8 *10 *11.
For n=8, 6652800 = 1*2*3*12*14*15*20*22 = 4 * 5 * 6 * 7 * 8 * 9 *10 *11. (End)
From _Zhao Hui Du_, May 11 2024: (Start)
For n=9, 133056000 = 1*2*3*9*14*16*20*22*25 = 4*5*6*7*8*10*11*12*15.
For n=10, 2075673600 = 1*2*3*7*15*16*18*20*22*26 = 4*5*6*8*9*10*11*12*13*14. (End)
		

Crossrefs

Extensions

a(7)-a(8) from Jinyuan Wang, May 31 2022
a(9)-a(10) from Zhao Hui Du, May 11 2024
a(11)-a(20) from Jon E. Schoenfield, May 11 2024
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