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A124144 Perfect powers pp such that sigma(n)=pp for some abundant number n. 0


%S 144,216,576,784,961,1296,1728,1764,2304,2744,3136,3600,3844,4356,

%T 5184,6084,7056,7776,8100,9216,11664,12544,13824,14400,15376,15876,

%U 17424,19600,20736,21952,24336,28224

%N Perfect powers pp such that sigma(n)=pp for some abundant number n.

%e a(1)=144 since sigma(66)=144>2*66=132.

%p with(numtheory); egcd := proc(n::posint) 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 s>2*n and egcd(s)>1 then print(n,s,ifactor(s)); L:=[op(L),n]; P:=P union {s}; fi od od; L; P;

%Y Cf. A001597, A005101, A065496.

%K nonn

%O 1,1

%A _Walter Kehowski_, Dec 01 2006

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Last modified December 14 17:44 EST 2019. Contains 329979 sequences. (Running on oeis4.)