A048257 Integers whose sum of divisors is a 7th power.

1, 93, 127, 11811, 112890, 120054, 124338, 127330, 132770, 133998, 134090, 137058, 138754, 139962, 146710, 148665, 148810, 149534, 153986, 155510, 160215, 161194, 164985, 167134, 170986, 173098, 183687, 184682, 187143, 191913, 198485, 206823, 206965, 207687

Offset

1,2

Comments

If m and n are coprime members of the sequence, then m*n is also a member. - Robert Israel, May 10 2018

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(a(n)) = x^7, where the initial values of x are 1, 2, 4, 6 (48 times), ...

Example

Divisors(11811) = {1,3,31,93,127,381,3937,11811} and sigma(11811) = 16384 = 4^7.

Maple

filter:= n -> type(map(t -> t[2]/7, ifactors(numtheory:-sigma(n))[2]), list(integer)):
select(filter, [$1..21*10^4]); # Robert Israel, May 09 2018

Mathematica

Select[Range[210000], IntegerQ[Surd[DivisorSigma[1, #], 7]]&] (* Harvey P. Dale, Jun 09 2017 *)

Prog

(PARI) isok(n) = ispower(sigma(n), 7); \\ Michel Marcus, Dec 20 2013

Crossrefs

Cf. A000203, A006532, A020477, A019422, A019423, A019424, A048251-A048256, A048258.

Sequence in context: A082131 A249300 A153684 * A255991 A213114 A250366

Adjacent sequences: A048254 A048255 A048256 * A048258 A048259 A048260

Keyword

nonn

Author

Labos Elemer

Status

approved