A269045 -id:A269045 - cp's OEIS frontend

A328045 a(n) = smallest m for which there is a sequence n = b_1 < b_2 < ... < b_t = m such that b_1^c_1b_2^c_2...*b_t^c_t is a fourth power, with all c_i < 4.

0, 1, 4, 6, 4, 10, 9, 14, 15, 9, 18, 22, 20, 26, 21, 24, 16, 34, 27, 38, 25, 28, 33, 46, 30, 25, 39, 35, 36, 58, 40, 62, 42, 44, 51, 45, 36, 74, 57, 52, 49, 82, 50, 86, 55, 54, 69, 94, 54, 49, 63, 68, 65, 106, 70, 66, 64, 76, 87, 118, 75, 122, 93, 77, 64, 78

Offset: 0

Peter Kagey, Oct 02 2019

nonn

a(n) = n if and only if n is a perfect square.
a(n) >= n + A300518(n) if n is not a perfect square.
a(n) <= A006255(n), and a(n) = A006255(n) except for when n is in A328218, a subsequence of A269045.

			For n = 1, a(1) = 1   with sequence 1                =  1^4.
For n = 2, a(2) = 4   with sequence 2^2 * 4          =  2^4.
For n = 3, a(3) = 6   with sequence 3^2 * 4   *  6^2 =  6^4.
For n = 4, a(4) = 4   with sequence 4^2              =  2^4.
For n = 5, a(5) = 10  with sequence 5   * 8^3 * 10^3 = 40^4.
For n = 6, a(6) = 9   with sequence 6^2 * 8^2 *  9   = 12^4.
For n = 7, a(7) = 14  with sequence 7^2 * 8^2 * 14^2 = 28^4.

Peter Kagey, Table of n, a(n) for n = 0..500

Cf. A006255 (square), A277494 (cube).

Cf. A269045, A300518, A328218.

A328218 Numbers k for which A006255(k) > A328045(k).

Original entry on oeis.org

2, 3, 6, 20, 24, 28, 30, 32, 35, 40, 42, 45, 56, 84, 90, 91, 99, 108, 110, 120, 126, 143, 150, 156, 165, 171, 180, 182, 189, 195, 198, 210, 220, 224, 231, 243, 245, 272, 280, 285, 294, 304, 312, 315, 323, 330, 342, 350, 378, 405, 416, 420, 432, 455, 459, 460

Offset: 1

Peter Kagey, Oct 08 2019

nonn

This is a subsequence of A269045.

Cf. A006255, A269045, A328045.

cp's OEIS Frontend

A328045 a(n) = smallest m for which there is a sequence n = b_1 < b_2 < ... < b_t = m such that b_1^c_1b_2^c_2...*b_t^c_t is a fourth power, with all c_i < 4.

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A328218 Numbers k for which A006255(k) > A328045(k).

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cp's OEIS Frontend

A328045 a(n) = smallest m for which there is a sequence n = b_1 < b_2 < ... < b_t = m such that b_1^c_1*b_2^c_2*...*b_t^c_t is a fourth power, with all c_i < 4.

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Author

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Examples

Links

Crossrefs

A328218 Numbers k for which A006255(k) > A328045(k).

Views

Author

Keywords

Comments

Crossrefs

A328045 a(n) = smallest m for which there is a sequence n = b_1 < b_2 < ... < b_t = m such that b_1^c_1b_2^c_2...*b_t^c_t is a fourth power, with all c_i < 4.