A001476 Numbers that are not the sum of distinct positive cubes.

2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 66, 67, 68, 69, 70, 71, 74, 75, 76, 77, 78, 79, 80

Offset: 1

Author

Jeff Adams (jeff.adams(AT)byu.net)

Keywords

• nonn
• fini
• full

Comments

Complement of A003997.

There are 85 terms below 100, 793 terms below 1000, but only 2765 terms below 10^4, and only 23 more up to the largest term a(2788)=12758. - M. F. Hasler, Feb 25 2012

Indices k such that A279329(k) = 0. - Vaclav Kotesovec, Sep 22 2017

Links

• T. D. Noe, Table of n, a(n) for n = 1..2788 (complete sequence)
• R. E. Dressler and T. Parker, 12,758, Math. Comp. 28 (1974), 313-314.
• R. Sprague, Über Zerlegungen in n-te Potenzen mit lauter verschiedenen Grundzahlen, Math. Z. 51, (1948). 466-468.
• Eric Weisstein's World of Mathematics, Cubic Number

Crossrefs

Cf. A001422, A003997, A279329, A279486.

Programs

Mathematica

Cubes[ n_ ] := Block[ {A, i}, A = {0}; If[ n>0, Do[ A = Union[ A, A + i*i*i ], {i, n} ]; ]; Return[ A ]; ]; Q = Complement[ Table[ i, {i, 1, 12760} ], Cubes[ 23 ] ]

PARI

select( is_A001476(n,m=n)={m^3>n&&m=sqrtnint(n,3); n!=m^3&&!while(m>1, is_A001476(n-m^3, m--)||return)}, [1..77]) \\ M. F. Hasler, Apr 21 2020

Extensions

Definition clarified by Jeppe Stig Nielsen, Jan 27 2015