login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A048257 Integers whose sum of divisors is a 7th power. 6
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 17 23:21 EDT 2019. Contains 325109 sequences. (Running on oeis4.)