

A020477


Sum of divisors of n is a cube.


20



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.
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. A006532.
Sequence in context: A175345 A142358 A210684 * A203356 A223239 A140633
Adjacent sequences: A020474 A020475 A020476 * A020478 A020479 A020480


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



