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

0,3

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.

Links

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

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

Example

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

Crossrefs

Cf. A006255, A277278.

Sequence in context: A010404 A010447 A112082 * A174896 A304634 A319240

Adjacent sequences: A277491 A277492 A277493 * A277495 A277496 A277497

Keyword

nonn

Author

Peter Kagey, Oct 17 2016

Status

approved