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A124143 Perfect powers pp such that sigma(n)=pp for some positive integer n. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..46.

EXAMPLE

a(1)=4 since sigma(3)=4=2^2.

MAPLE

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;

MATHEMATICA

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 *)

PROG

(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

(MAGMA) Set(Sort([SumOfDivisors(k): k in[A065496(n)]])) // Jaroslav Krizek, Mar 10 2015

CROSSREFS

Cf. A001597, A065496.

Sequence in context: A162459 A129195 A180098 * A173617 A034041 A050442

Adjacent sequences:  A124140 A124141 A124142 * A124144 A124145 A124146

KEYWORD

nonn

AUTHOR

Walter Kehowski, Dec 01 2006

STATUS

approved

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Last modified December 12 17:59 EST 2019. Contains 329960 sequences. (Running on oeis4.)