A281364 Numbers n such that sigma(n^3) is the sum of two positive cubes.

21, 22, 55, 129, 511, 770, 1070, 1071, 1074, 1434, 1708, 1914, 2721, 2926, 3080, 4195, 4464, 4814, 4879, 5236, 5907, 6086, 6114, 7228, 7831, 8029, 8289, 9086, 10149, 10547, 11145, 12305, 12621, 13348, 14993, 15012, 16212, 17670, 19513, 20020, 20083

Offset

1,1

Comments

265247 is the first term that is prime; sigma(265247^3) = 18661780598460480 = 48432^3 + 264708^3. In other words, the equation (1 + p)*(1 + p^2) = a^3 + b^3 where p is prime and a, b > 0, is soluble.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..700

Example

21 is a term because sigma(21^3) = 16000 = 20^3 + 20^3.

Prog

(PARI) isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));
lista(nn) = for(n=1, nn, if(isA003325(sigma(n^3)), print1(n, ", ")));

Crossrefs

Cf. A000203, A000578, A003325, A175926.

Sequence in context: A041882 A286762 A301661 * A041900 A041902 A041898

Adjacent sequences: A281361 A281362 A281363 * A281365 A281366 A281367

Keyword

nonn

Author

Altug Alkan, May 01 2016

Status

approved