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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.

%I A328045 #31 Jan 02 2024 12:44:09
%S A328045 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,
%T A328045 25,39,35,36,58,40,62,42,44,51,45,36,74,57,52,49,82,50,86,55,54,69,94,
%U A328045 54,49,63,68,65,106,70,66,64,76,87,118,75,122,93,77,64,78
%N 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.
%C A328045 a(n) = n if and only if n is a perfect square.
%C A328045 a(n) >= n + A300518(n) if n is not a perfect square.
%C A328045 a(n) <= A006255(n), and a(n) = A006255(n) except for when n is in A328218, a subsequence of A269045.
%H A328045 Peter Kagey, <a href="/A328045/b328045.txt">Table of n, a(n) for n = 0..500</a>
%e A328045 For n = 1, a(1) = 1   with sequence 1                =  1^4.
%e A328045 For n = 2, a(2) = 4   with sequence 2^2 * 4          =  2^4.
%e A328045 For n = 3, a(3) = 6   with sequence 3^2 * 4   *  6^2 =  6^4.
%e A328045 For n = 4, a(4) = 4   with sequence 4^2              =  2^4.
%e A328045 For n = 5, a(5) = 10  with sequence 5   * 8^3 * 10^3 = 40^4.
%e A328045 For n = 6, a(6) = 9   with sequence 6^2 * 8^2 *  9   = 12^4.
%e A328045 For n = 7, a(7) = 14  with sequence 7^2 * 8^2 * 14^2 = 28^4.
%Y A328045 Cf. A006255 (square), A277494 (cube).
%Y A328045 Cf. A269045, A300518, A328218.
%K A328045 nonn
%O A328045 0,3
%A A328045 _Peter Kagey_, Oct 02 2019