A020477 - OEIS

%I #48 Oct 30 2023 07:22:14

%S 1,7,102,110,142,159,187,381,690,714,770,994,1034,1054,1065,1113,1164,

%T 1173,1265,1293,1309,1633,1643,2667,3638,3937,4505,4830,4855,5373,

%U 5671,5730,5997,6486,6517,6906,7130,7238,7378,7455,7755,7905,8148,8211,8426

%N Numbers whose sum of divisors is a cube.

%D David Wells, Curious and Interesting Numbers (Revised), Penguin Books, page 118.

%H K. D. Bajpai, <a href="/A020477/b020477.txt">Table of n, a(n) for n = 1..10800</a> (first 1000 terms from T. D. Noe)

%H Frits Beukers, Florian Luca and Frans Oort, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.119.05.373">Power Values of Divisor Sums</a>, The American Mathematical Monthly, Vol. 119, No. 5 (May 2012), pp. 373-380.

%H Carol Nelson, David E. Penney, Carl Pomerance, <a href="http://web.archive.org/web/20171112075614/http://www.trottermath.net/numthry/ruth714.html">714 and 715</a>, J. Recreational Mathematics 7(2), Spring 1974, 87-89 [copy from Wayback machine]

%H C. Nelson, D. E. Penney, and C. Pomerance (1974) <a href="http://www.trottermath.net/numthry/ruth714.html">714 and 715</a>, J. Recreational Mathematics 7(2), 87-89 (see top of page 89); <a href="http://www.math.dartmouth.edu/~carlp/714and715.pdf">alternative copy</a>. [Warning: As of March 2018 this site appears to have been hacked. Proceed with great caution. The original content should be retrieved from the Wayback machine and added here. - _N. J. A. Sloane_, Mar 29 2018]

%e Factor 381; divisors are 1, 3, 127, 381. Sum is 512. Integral cube root of n is 8. So 381 is in sequence.

%t Do[If[IntegerQ[DivisorSigma[1, n]^(1/3)], Print[n]], {n, 1, 10^4}]

%t Select[Range[10000],IntegerQ[Surd[DivisorSigma[1,#],3]]&] (* _Harvey P. Dale_, Nov 16 2014 *)

%o (PARI) isok(n) = ispower(sigma(n), 3); \\ _Michel Marcus_, Jul 03 2014

%Y Cf. A000203, A006532.

%K nonn

%O 1,2

%A _David W. Wilson_