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%I #31 Feb 15 2019 18:45:52
%S 8,9,14,26,38,62,74,86,122,134,146,158,194,206,218,254,278,302,314,
%T 326,362,386,398,422,446,458,482,542,554,566,614,626,662,674,698,734,
%U 746,758,794,818,842,866,878,914,926,974,998,1046,1082,1094,1142,1154,1202,1214
%N Sequence lists numbers k > 1 such that k^2 == d(k) (mod sigma(k)), where d = A000005 and sigma = A000203.
%C A112772 is a subsequence. After 8 and 9, the following numbers not in A112772 are 5438, 5462, 5504, 11096, ...
%H Jinyuan Wang, <a href="/A323249/b323249.txt">Table of n, a(n) for n = 1..10000</a>
%F Solutions of k^2 mod sigma(k) = d(k).
%e sigma(8) = 15 and 8^2 mod 15 = 4 = d(8).
%p with(numtheory): op(select(n->n^2 mod sigma(n)=tau(n),[$1..1214]));
%t Select[Range[1225], PowerMod[#1, 2, #3] == #2 & @@ Prepend[DivisorSigma[{0, 1}, #], #] &] (* _Michael De Vlieger_, Jan 18 2019 *)
%o (PARI) for(k=1, 2000, x=sigma(k); if(Mod(k,x)^2==Mod(numdiv(k), x), print1(k, ", "))) \\ _Jinyuan Wang_, Feb 03 2019
%Y Cf. A000005, A000203, A112772, A323250, A323251.
%K nonn,easy
%O 1,1
%A _Paolo P. Lava_, Jan 08 2019
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