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%I #22 Dec 16 2022 09:01:22
%S 1,3,5,9,15,25,27,45,55,75,81,125,135,165,171,225,243,275,375,405,495,
%T 513,605,625,675,729,825,855,1125,1215,1375,1485,1539,1815,1875,2025,
%U 2187,2475,2565,3025,3125,3249,3375,3645,4125,4275,4455,4617,4965,5445
%N Numbers k that divide 10^k + 5^k.
%H G. C. Greubel, <a href="/A045599/b045599.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[Range[5500], Mod[PowerMod[10,#,#] +PowerMod[5,#,#],#]==0 &] (* _G. C. Greubel_, Dec 12 2022 *)
%o (Magma) [n: n in [1..5500] | (Modexp(10,n,n) + Modexp(5,n,n)) mod n eq 0 ]; // _G. C. Greubel_, Dec 12 2022
%o (SageMath) [n for n in (1..5500) if (power_mod(10,n,n)+power_mod(5,n,n))%n==0 ] # _G. C. Greubel_, Dec 12 2022
%o (PARI) is(n)=(Mod(10,n)^n+Mod(5,n)^n==0);
%o for(n=1,5500,if(is(n),print1(n,", "))); \\ _Joerg Arndt_, Dec 13 2022
%Y Cf. A000351, A011557.
%K nonn
%O 1,2
%A _David W. Wilson_