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A277494 a(n) = smallest m for which there is a sequence n = b_1 < b_2 <= b_3 <= ... <= b_t = m such that b_1*b_2*...*b_t is a perfect cube.

%I A277494 #28 May 02 2017 22:17:18
%S A277494 0,1,4,6,9,10,12,14,8,16,15,22,18,26,21,20,24,34,25,38,28,30,33,46,32,
%T A277494 35,39,27,36,58,40,62,45,44,51,42,48,74,57,52,50,82,49,86,55,54,69,94,
%U A277494 60,56,63,68,65,106,70,66,72,76,87,118,75,122,93,77,64,78
%N A277494 a(n) = smallest m for which there is a sequence n = b_1 < b_2 <= b_3 <= ... <= b_t = m such that b_1*b_2*...*b_t is a perfect cube.
%C A277494 A cube analog of R. L. Graham's sequence (A006255).
%C A277494 Like R. L. Graham's sequence, this is a bijection between the natural numbers and the nonprimes.
%C A277494 a(p) = 2p for all primes p.
%H A277494 Peter Kagey, <a href="/A277494/b277494.txt">Table of n, a(n) for n = 0..5000</a>
%H A277494 Peter Kagey, <a href="/A277494/a277494.txt">Examples of a(n) for n = 0..1000</a>
%e A277494 a(0)  = 0  via 0                     =   0^3
%e A277494 a(1)  = 1  via 1                     =   1^3
%e A277494 a(2)  = 4  via 2 * 4                 =   2^3
%e A277494 a(3)  = 6  via 3 * 4^2 * 6^2         =  12^3
%e A277494 a(4)  = 9  via 4 * 6 * 9             =   6^3
%e A277494 a(5)  = 10 via 5 * 6 * 9 * 10^2      =  30^3
%e A277494 a(6)  = 12 via 6 * 9^2 * 12          =  18^3
%e A277494 a(7)  = 14 via 7 * 9^2 * 12^2 * 14^2 = 252^3
%e A277494 a(8)  = 8  via 8                     =   2^3
%e A277494 a(9)  = 16 via 9 * 12 * 16           =  12^3
%e A277494 a(10) = 15 via 10 * 12 * 15^2        =  30^3
%Y A277494 Cf. A006255, A277278.
%K A277494 nonn
%O A277494 0,3
%A A277494 _Peter Kagey_, Oct 17 2016