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A281364
Numbers n such that sigma(n^3) is the sum of two positive cubes.
1
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
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
KEYWORD
nonn
AUTHOR
Altug Alkan, May 01 2016
STATUS
approved