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

Author

Labos Elemer

Keywords

• nonn

Comments

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

Examples

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

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.

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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