The On-Line Encyclopedia of Integer Sequences (OEIS)

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A281364

Numbers n such that sigma(n^3) is the sum of two positive cubes.
(history; published version)

#7 by Bruno Berselli at Thu Feb 02 02:42:09 EST 2017

STATUS

reviewed

approved

#6 by Joerg Arndt at Thu Feb 02 02:26:50 EST 2017

STATUS

proposed

reviewed

#5 by Chai Wah Wu at Wed Feb 01 23:27:32 EST 2017

STATUS

editing

proposed

#4 by Chai Wah Wu at Wed Feb 01 23:27:11 EST 2017

LINKS

Chai Wah Wu, <a href="/A281364/b281364.txt">Table of n, a(n) for n = 1..700</a>

STATUS

approved

editing

#3 by N. J. A. Sloane at Fri Jan 27 18:19:48 EST 2017

STATUS

editing

approved

#2 by N. J. A. Sloane at Fri Jan 27 18:19:45 EST 2017

NAME

allocated for N. J. A. Sloane

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

DATA

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.

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.

KEYWORD

allocated

nonn

AUTHOR

Altug Alkan, May 01 2016

STATUS

approved

editing

#1 by N. J. A. Sloane at Fri Jan 20 15:30:50 EST 2017

NAME

allocated for N. J. A. Sloane

KEYWORD

allocated

STATUS

approved