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A065496
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Numbers n such that sigma(n) is a nontrivial power, i.e. sigma(n) = a^b where a and b are greater than 1.
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10
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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; internal format)
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OFFSET
| 1,1
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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. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), May 10 2010]
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EXAMPLE
| sigma(21) = 2^5, sigma(22) = 6^2, sigma(94) = 12^2.
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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
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CROSSREFS
| Cf. A000203, A046528.
Sequence in context: A196035 A196038 A180097 * A018479 A090504 A018548
Adjacent sequences: A065493 A065494 A065495 * A065497 A065498 A065499
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KEYWORD
| nonn
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Nov 24 2001
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 25 2001
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