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A180162 a(n) is the smallest number N such that sigma(N) is an n-th power but not a higher power, with a(n) = 0 if no such number exists.

%I A180162 #10 Feb 13 2018 12:59:23
%S A180162 1,2,3,7,510,21,17490,93,217,381,651,118879530,2667,8191,11811,24573,
%T A180162 57337,82677,172011,393213,761763,1572861,2752491,5332341,11010027,
%U A180162 21845397,48758691,85327221,199753347,341310837,677207307,1398273429
%N A180162 a(n) is the smallest number N such that sigma(N) is an n-th power but not a higher power, with a(n) = 0 if no such number exists.
%H A180162 Ray Chandler, <a href="/A180162/b180162.txt">Table of n, a(n) for n = 0..469</a>
%F A180162 a(n) >= A063869(n). - _R. J. Mathar_, Aug 20 2010
%e A180162 a(4)=510 since 510=2*3*5*17, sigma(510)=2^4*3^4.
%e A180162 a(11)=2*3*5*7*11*53*971=118879530 since sigma(118879530)=6^11.
%p A180162 with(numtheory);
%p A180162 egcd:=proc(n::posint) local L; if n>1 then L:=ifactors(n)[2]; L:=map(z-> z[2],L); igcd(op(L)) else 0 fi end:
%p A180162 P:={}: SP:={}:
%p A180162 for w to 1 do
%p A180162 for n from 1 to 12^6 do
%p A180162 sn:=sigma(n);
%p A180162 esn:=egcd(sn);
%p A180162 if not esn in P then
%p A180162 P:=P union {esn};
%p A180162 SP:=SP union {[esn,n]};
%p A180162 printf("n=%d, esn=%d, sn=...\n",n,esn);
%p A180162 print(ifactor(sn));
%p A180162 fi;
%p A180162 od; #n
%p A180162 od; #w
%p A180162 P; SP;
%Y A180162 Cf. A065496, A000203, A175432, A169981.
%K A180162 nonn
%O A180162 0,2
%A A180162 _Walter Kehowski_, Aug 14 2010, Aug 19 2010
%E A180162 a(11) found by _Walter Kehowski_ and Artur Jasinski, Aug 16 2010
%E A180162 Edited by _N. J. A. Sloane_, Aug 19 2010
%E A180162 a(23) onwards from _Ray Chandler_, Aug 19 2010