

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.


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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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,more


AUTHOR

Peter Kagey, Oct 02 2019


STATUS

approved



