cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A020477 Numbers whose sum of divisors is a cube.

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%I A020477 #50 Jun 05 2025 13:43:44
%S A020477 1,7,102,110,142,159,187,381,690,714,770,994,1034,1054,1065,1113,1164,
%T A020477 1173,1265,1293,1309,1633,1643,2667,3638,3937,4505,4830,4855,5373,
%U A020477 5671,5730,5997,6486,6517,6906,7130,7238,7378,7455,7755,7905,8148,8211,8426
%N A020477 Numbers whose sum of divisors is a cube.
%D A020477 David Wells, Curious and Interesting Numbers (Revised), Penguin Books, page 118.
%H A020477 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 A020477 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 A020477 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 A020477 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>.
%e A020477 Factor 381; divisors are 1, 3, 127, 381. Sum is 512. Integral cube root of n is 8. So 381 is in sequence.
%t A020477 Do[If[IntegerQ[DivisorSigma[1, n]^(1/3)], Print[n]], {n, 1, 10^4}]
%t A020477 Select[Range[10000],IntegerQ[Surd[DivisorSigma[1,#],3]]&] (* _Harvey P. Dale_, Nov 16 2014 *)
%o A020477 (PARI) isok(n) = ispower(sigma(n), 3); \\ _Michel Marcus_, Jul 03 2014
%Y A020477 Cf. A000203, A006532.
%K A020477 nonn
%O A020477 1,2
%A A020477 _David W. Wilson_