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.

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

0,3

Comments

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.

Links

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

Example

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.

Crossrefs

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

Cf. A269045, A300518, A328218.

Sequence in context: A349093 A143545 A338155 * A277278 A328722 A143521

Adjacent sequences: A328042 A328043 A328044 * A328046 A328047 A328048

Keyword

nonn

Author

Peter Kagey, Oct 02 2019

Status

approved