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Search: id:A066109
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| A066109 |
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Sigma4(n)/Sigma2(n) is prime. |
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+0
5
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| 4, 9, 20, 25, 169, 289, 961, 1849, 3721, 6889, 11881, 14641, 15625, 17161, 52441, 57121, 66049, 69169, 72361, 96721, 97969, 117649, 130321, 196249, 214369, 253009, 326041, 351649, 358801, 383161, 410881, 418609, 426409, 434281, 491401
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OFFSET
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1,1
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COMMENT
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Except for 3rd term 20, below 10000000 all other entries are even powers of a prime. These primes are listed in A066111. It is not known if other numbers similar to 20 exist or not.
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FORMULA
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A001159[n]/A001157[n] is prime.
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EXAMPLE
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m = 20: divisors[20] = {20, 10, 5, 4, 2, 1}, Sigma4 = 160000+10000+625+256+16+1 = 170898, Sigma2 = 400+100+25+16+4+1 = 546; p = 170898/546 = 73 is prime.
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MATHEMATICA
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Do[s = DivisorSigma[4, n]; z = DivisorSigma[2, n]; If[PrimeQ[s/z], Print[{n, s, z, s/z}]], {n, 1, 10000000}]
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CROSSREFS
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Cf. A001159, A001157, A000040.
Sequence in context: A115075 A063454 A053807 this_sequence A030734 A073360 A075385
Adjacent sequences: A066106 A066107 A066108 this_sequence A066110 A066111 A066112
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Dec 05 2001
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