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A328143 Number of sequences [(b_1, c_1),...,(b_t, c_t)] such that n = b_1 < b_2 < ... < b_t = A328045(n), all c_i are positive integers less than 4, and b_1^c_1*b_2^c_2*...*b_t^c_t is a fourth power. 0

%I

%S 3,3,2,2,1,12,2,12,12,1,12,192,12,768,12,12,3,12288,12,49152,2,6,48

%N Number of sequences [(b_1, c_1),...,(b_t, c_t)] such that n = b_1 < b_2 < ... < b_t = A328045(n), all c_i are positive integers less than 4, and b_1^c_1*b_2^c_2*...*b_t^c_t is a fourth power.

%C When does a(n) = 3*4^A260510(n)? It does for n = 0, 1, 5, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, ...

%C a(n) = 1 if n is square but not a fourth power.

%C a(k^4) = 3.

%C a(24) = 2, a(25) = 1, a(26) = 48, a(27) = 3, and a(28) = 2.

%e For n = 21 the a(21) = 6 solutions are

%e 21^2 * 27^2 * 28^2 = 126^4,

%e 21^3 * 24^2 * 27^1 * 28^1 = 252^4,

%e 21^2 * 25^2 * 27^2 * 28^2 = 630^4,

%e 21^3 * 24^2 * 25^2 * 27^1 * 28^1 = 1260^4,

%e 21^1 * 24^2 * 27^3 * 28^3 = 1512^4, and

%e 21^1 * 24^2 * 25^2 * 27^3 * 28^3 = 7560^4.

%Y Cf. A006255, A260510, A277494, A328045.

%Y A259527 is the analog for squares.

%K nonn,more

%O 0,1

%A _Peter Kagey_, Oct 04 2019

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Last modified August 13 08:18 EDT 2022. Contains 356079 sequences. (Running on oeis4.)