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%I #20 Mar 14 2017 11:28:33
%S 1,7,121,2,91,9,3,847,12667700813876161,7,14,32,116281,1729,343,4,63,
%T 242,47,21,1369,79,11011,2048,22,88673905697133127,4826809,961,7,
%U 4782969,13,182,363,29,224,25,16,813967,18,23,53599,3486784401,1532791798479015481,4459
%N Smallest k such that 2n - 1 divides sigma(k^2), or 0 if no such k exists.
%e a(3)=121 because 3*2 - 1 = 5 divides sigma(121^2) = 16105, and sigma(n^2) is not divisible by 5 for n < 121.
%o (PARI) a(n) = my(k = 1); while(1,if(sigma(k^2)%(2*n - 1)==0, return(k), k+=1)); \\ _Indranil Ghosh_, Mar 13 2017
%Y Cf. A000203, A070982, A227470.
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, Mar 12 2017
%E a(9), a(26), a(42)-a(44) from _Giovanni Resta_, Mar 12 2017