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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
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
Sequence in context: A082131 A249300 A153684 * A255991 A213114 A250366
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified February 27 19:24 EST 2024. Contains 370378 sequences. (Running on oeis4.)