

A020477


Numbers whose sum of divisors is a cube.


25



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
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OFFSET

1,2


REFERENCES

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


LINKS

T. D. Noe and 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. 373380.
Carol Nelson, David E. Penney, Carl Pomerance, 714 and 715, J. Recreational Mathematics 7(2), Spring 1974, 8789 [copy from Wayback machine]
C. Nelson, D. E. Penney, and C. Pomerance (1974) 714 and 715, J. Recreational Mathematics 7(2), 8789 (see top of page 89); alternative copy. [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]


EXAMPLE

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


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 *)


PROG

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


CROSSREFS

Cf. A000203, A006532.
Sequence in context: A210684 A357334 A329239 * A348887 A203356 A346719
Adjacent sequences: A020474 A020475 A020476 * A020478 A020479 A020480


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



