A020477 Numbers whose sum of divisors is a cube.

1, 7, 102, 110, 142, 159, 187, 381, 690, 714, 770, 994, 1034, 1054, 1065, 1113, 1164, 1173, 1265, 1293, 1309, 1633, 1643, 2667, 3638, 3937, 4505, 4830, 4855, 5373, 5671, 5730, 5997, 6486, 6517, 6906, 7130, 7238, 7378, 7455, 7755, 7905, 8148, 8211, 8426

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Examples

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

References

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

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..10800 (first 1000 terms from T. D. Noe)
• Frits Beukers, Florian Luca and Frans Oort, Power Values of Divisor Sums, The American Mathematical Monthly, Vol. 119, No. 5 (May 2012), pp. 373-380.
• Carol Nelson, David E. Penney, Carl Pomerance, 714 and 715, J. Recreational Mathematics 7(2), Spring 1974, 87-89 [copy from Wayback machine]
• C. Nelson, D. E. Penney, and C. Pomerance (1974) 714 and 715, J. Recreational Mathematics 7(2), 87-89 (see top of page 89); alternative copy.

Crossrefs

Cf. A000203, A006532.

Programs

Mathematica

Do[If[IntegerQ[DivisorSigma[1, n]^(1/3)], Print[n]], {n, 1, 10^4}]
Select[Range[10000],IntegerQ[Surd[DivisorSigma[1,#],3]]&] (* Harvey P. Dale, Nov 16 2014 *)

PARI

isok(n) = ispower(sigma(n), 3); \\ Michel Marcus, Jul 03 2014