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A124143
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Perfect powers pp such that sigma(k) = pp for some positive integer k.
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1
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4, 8, 32, 36, 121, 128, 144, 216, 256, 324, 400, 512, 576, 784, 900, 961, 1024, 1296, 1600, 1728, 1764, 1936, 2304, 2704, 2744, 2916, 3136, 3600, 3844, 4096, 4356, 4624, 4900, 5184, 5776, 5832, 6084, 6400, 7056, 7744, 7776, 8000, 8100, 8192, 9216, 9604
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(1) = 4 since sigma(3) = 4 = 2^2.
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MAPLE
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with(numtheory); egcd := proc(n) local L; if n>1 then L:=ifactors(n)[2]; L:=map(z->z[2], L); return igcd(op(L)) else return 1 fi; end; L:=[]: P:={}: for w to 1 do for n from 1 to 10000 do s:=sigma(n); if egcd(s)>1 then print(n, s, ifactor(s)); L:=[op(L), n]; P:=P union {s}; fi od od; L; P;
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MATHEMATICA
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powerQ[n_] := Block[{pf = FactorInteger@ n, min}, min = Min @@ Last /@ pf; min > 1 && AllTrue[Last /@ pf/min, IntegerQ]]; lim = 10000; Intersection[Select[Range@ lim, powerQ], DeleteDuplicates@ Sort[DivisorSigma[1, #] & /@ Range@ lim]] (* Michael De Vlieger, Mar 10 2015 *)
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PROG
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(Magma) Set(Sort([SumOfDivisors(k): k in[1..10000], b in [2..15], a in [2..100] | SumOfDivisors(k) eq a^b])); // Jaroslav Krizek, Mar 10 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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