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%I #17 Jul 14 2020 07:04:36
%S 2401,9604,21609,28561,38416,60025,86436,114244,130321,153664,194481,
%T 240100,257049,290521,345744,456976,521284,540225,614656,693889,
%U 714025,777924,923521,960400,1028196,1162084,1172889,1270129,1382976,1500625
%N Solutions to mod(sigma(x), 6) = 5.
%H Amiram Eldar, <a href="/A074384/b074384.txt">Table of n, a(n) for n = 1..1000</a>
%F {n: A084301(n) = 5}. - _R. J. Mathar_, May 19 2020
%e 4th powers of primes of the form 6k+1 are here because sigma[p^4]=p^4+p^3+p^2+p+1 congruent 1+1+1+1+1=5 mod 6. There are also other fourth powers, like 38416=(2*7)^4, 194481=(3*7)^4, 456976=(2*13)^4, and solutions which are not fourth powers like 9604=2^2*7^4 and 21609=3^2*7^4.
%t Do[s=Mod[DivisorSigma[1, n], 6]; If[s==5, Print[n]], {n, 1, 1000000}]
%t Select[Range[1600000],Mod[DivisorSigma[1,#],6]==5&] (* _Harvey P. Dale_, Jul 06 2014 *)
%Y Cf. A000203, A072862, A072461, A072462.
%K nonn
%O 1,1
%A _Labos Elemer_, Aug 22 2002