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A048258 Integers whose sum of divisors is an 8th power. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A221427 A086026 A100794 * A013541 A167912 A038662

Adjacent sequences:  A048255 A048256 A048257 * A048259 A048260 A048261

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved

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Last modified July 23 11:44 EDT 2019. Contains 325254 sequences. (Running on oeis4.)