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.

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, 35, 39, 27, 36, 58, 40, 62, 45, 44, 51, 42, 48, 74, 57, 52, 50, 82, 49, 86, 55, 54, 69, 94, 60, 56, 63, 68, 65, 106, 70, 66, 72, 76, 87, 118, 75, 122, 93, 77, 64, 78

Offset: 0

Author

Peter Kagey, Oct 17 2016

Keywords

• nonn

Comments

A cube analog of R. L. Graham's sequence (A006255).

Like R. L. Graham's sequence, this is a bijection between the natural numbers and the nonprimes.

a(p) = 2p for all primes p.

Examples

			a(0)  = 0  via 0                     =   0^3
a(1)  = 1  via 1                     =   1^3
a(2)  = 4  via 2 * 4                 =   2^3
a(3)  = 6  via 3 * 4^2 * 6^2         =  12^3
a(4)  = 9  via 4 * 6 * 9             =   6^3
a(5)  = 10 via 5 * 6 * 9 * 10^2      =  30^3
a(6)  = 12 via 6 * 9^2 * 12          =  18^3
a(7)  = 14 via 7 * 9^2 * 12^2 * 14^2 = 252^3
a(8)  = 8  via 8                     =   2^3
a(9)  = 16 via 9 * 12 * 16           =  12^3
a(10) = 15 via 10 * 12 * 15^2        =  30^3
		

Links

• Peter Kagey, Table of n, a(n) for n = 0..5000
• Peter Kagey, Examples of a(n) for n = 0..1000

Crossrefs

Cf. A006255, A277278.