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

Author

Altug Alkan, May 01 2016

Keywords

• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A000203, A000578, A003325, A175926.

Programs

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, ", ")));