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A329732 a(n) = smallest m for which there is a sequence n = b_1 < b_2 < ... < b_t = m such that b_1*b_2*...*b_t is a perfect cube. 1
0, 1, 4, 9, 9, 18, 18, 21, 8, 16, 24, 33, 18, 39, 28, 30, 25, 51, 25, 57, 36, 36, 44, 69, 42, 36, 52, 27, 45, 87, 45, 93, 49, 55, 68, 60, 48, 111, 76, 65, 60, 123 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(p) = 3*p for all odd primes p.

Conjecture: for each k there exists a sufficiently large N such that for all primes p > N, a(k*p) = (k+2)*p.

LINKS

Table of n, a(n) for n=0..41.

EXAMPLE

For n = 22, one increasing sequence starting with 22, ending with a(22) = 44, and having a product which is a perfect cube is

22 * 24 * 25 * 30  * 32 * 33 * 44 = 2640^3.

CROSSREFS

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

Cf. A277494.

Sequence in context: A065737 A014719 A139417 * A298816 A095873 A141801

Adjacent sequences:  A329729 A329730 A329731 * A329733 A329734 A329735

KEYWORD

nonn,more

AUTHOR

Peter Kagey, Nov 19 2019

STATUS

approved

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Last modified May 9 19:47 EDT 2021. Contains 343746 sequences. (Running on oeis4.)