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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 Cf. A000203, A046528. Sequence in context: A196035 A196038 A180097 * A322922 A018479 A335411 Adjacent sequences: A065493 A065494 A065495 * A065497 A065498 A065499 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.)