A338160 -id:A338160 - cp's OEIS frontend

A338159 The least number which can be represented as a product of the greatest number of distinct positive integers in exactly n ways.

1, 12, 60, 96, 360, 576, 480, 15120, 864, 2880, 3360, 6912, 25200, 7680, 20160, 36960, 4320, 93312, 46080, 82944, 221760, 34560, 2494800, 311040, 53760, 88200, 15966720, 30240, 3880800, 1995840, 43200, 322560, 388800, 345600, 970200, 241920, 414720, 5832000, 529200, 5598720

Offset: 1

Vladimir Letsko, Oct 14 2020

nonn

k = p_1^2*p_2*...*p_n obviously has exactly n required representations. Hence a(n) exists for any n.
a(n) is the least k such that A338160(k) = n.
All terms are in A025487.

			a(60) = 3 because 60 = 2*3*10 = 2*5*6 = 3*4*5 and each number less than 60 does not have exactly 3 such representations (adding the factor 1 to each product doesn't change anything).

David A. Corneth, Table of n, a(n) for n = 1..1283 (first 150 terms from Dmitry Khomovsky)
David A. Corneth, More terms

Cf. A338160.

a(A338160(n)) = n.

A338160(k) <> n for k < a(n).

a(23)-a(40) from Andrew Howroyd, Oct 14 2020

A340033 a(n) is the largest number of distinct numbers whose product is A025487(n).

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 3, 4, 4, 3, 4, 4, 4, 4, 4, 4, 5, 4, 5, 5, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 4, 5, 6, 5, 6, 5, 5, 6, 5, 6, 6, 6, 6, 6, 5, 6, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 6, 7, 6, 6, 7, 6, 6, 7, 7, 6, 7, 7, 6, 6, 5, 7, 6, 7, 7, 7, 7, 7, 6

Offset: 1

David A. Corneth, Feb 04 2021

nonn

			a(11) = 4 as A025487(11) = 36, which can be expressed as a product of at most 4 distinct positive integers via 1 * 2 * 3 * 6.

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A025487, A338160.

A340034 a(n) is the number of ways to represent A025487(n) as a product of the largest possible number of distinct factors in the product.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 3, 1, 3, 4, 1, 1, 1, 1, 1, 1, 1, 3, 2, 2, 5, 2, 4, 4, 7, 3, 6, 1, 4, 1, 9, 7, 1, 1, 1, 1, 1, 1, 3, 7, 4, 2, 2, 3, 1, 6, 2, 1, 7, 3, 10, 1, 11, 5, 9, 7, 2, 17, 5, 5, 1, 9, 11, 1, 2, 10, 1, 1, 12, 1, 1, 14, 9, 3, 2, 10, 1, 4, 1

Offset: 1

David A. Corneth, Feb 04 2021

			a(13) = 3 as there are three ways to represent A025487(13) = 60 as a product of largest possible number of distinct factors in the product. That number is 4 and the products are 1 * 2 * 3 * 10 = 1 * 2 * 5 * 6 = 1 * 3 * 4 * 5 = 60.

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A025487, A338160.

cp's OEIS Frontend

A338159 The least number which can be represented as a product of the greatest number of distinct positive integers in exactly n ways.

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A340033 a(n) is the largest number of distinct numbers whose product is A025487(n).

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A340034 a(n) is the number of ways to represent A025487(n) as a product of the largest possible number of distinct factors in the product.

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Author

Keywords

Examples

Links

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