A048258 Integers whose sum of divisors is an 8th power.

1, 217, 57337, 600270, 621690, 669990, 685290, 693294, 693770, 699810, 725934, 747670, 769930, 774894, 782598, 805970, 813378, 823938, 835670, 839802, 854930, 865490, 873334, 895594, 918435, 920414, 923410, 931634, 935715, 959565, 965174, 969034, 969206

Offset

1,2

Links

Donovan Johnson, Table of n, a(n) for n = 1..1000

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.

Formula

Sigma(1, a(n)) = x^8, where the initial values of x are 1, 2, 4, 6 (occurs 85 times), ...

Example

Divisors(217) = {1,7,31,217}, sum = 256 = 2^8.
Divisors(57337) = {1,7,8191,57337}, sum = 65536 = 4^8.
Divisors(1676377) = {1,647,2591,1676377}, sum = 1679616 = 6^8.

Mathematica

Select[Range[10^6], IntegerQ@ Surd[DivisorSigma[1, #], 8] &] (* Michael De Vlieger, Aug 01 2017, after Harvey P. Dale at A048257 *)

Prog

(PARI) isok(n) = ispower(sigma(n), 8); \\ Michel Marcus, Dec 30 2013

Crossrefs

Cf. A006532, A020477, A019422, A019423, A019424, A048251-A048257.

Sequence in context: A086026 A375816 A100794 * A373762 A013541 A352468

Adjacent sequences: A048255 A048256 A048257 * A048259 A048260 A048261

Keyword

nonn

Author

Labos Elemer

Status

approved