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A065496 Numbers n such that sigma(n) is a nontrivial power, i.e., sigma(n) = a^b where a and b are greater than 1. 12
3, 7, 21, 22, 31, 66, 70, 81, 93, 94, 102, 110, 115, 119, 127, 142, 159, 170, 187, 210, 214, 217, 265, 282, 310, 322, 343, 345, 357, 364, 381, 382, 385, 400, 472, 497, 510, 517, 527, 642, 651, 679, 690, 710, 714, 742, 745, 770, 782, 795, 820, 862, 884, 889 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Probably an unsolved problem: what numbers can appear as bases in the representations of sigma(n) as nontrivial powers?
A175432(a(n)) > 1 for n >= 1. - Jaroslav Krizek, May 10 2010
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
sigma(21) = 2^5, sigma(22) = 6^2, sigma(94) = 12^2.
MATHEMATICA
Do[s = DivisorSigma[1, n]; If[ Position[ Union[ Transpose[ FactorInteger[s]] [[2]]], 1] != {{1}} && Union[ Mod[ Union[ Transpose[ FactorInteger[s]] [[2]]], Union[ Transpose[ FactorInteger[s]] [[2]]] [[1]]]] == {0}, Print[n]], {n, 2, 10^3} ] (* Robert G. Wilson v, Nov 26 2001 *)
PROG
(PARI) is(n)=ispower(sigma(n)) \\ Charles R Greathouse IV, Mar 09 2014
CROSSREFS
Sequence in context: A196035 A196038 A180097 * A322922 A018479 A335411
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Nov 24 2001
EXTENSIONS
More terms from Vladeta Jovovic, Nov 25 2001
STATUS
approved

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Last modified May 29 11:40 EDT 2024. Contains 372940 sequences. (Running on oeis4.)