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Numbers k such that the base-10 representation of sigma(k) is a cyclic permutation of the base-10 representation of k.
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%I #10 Jul 24 2021 02:27:58

%S 1,69,609,196833,241605,440503,2374119,2841633,3256479,5529975

%N Numbers k such that the base-10 representation of sigma(k) is a cyclic permutation of the base-10 representation of k.

%e sigma(196833) = 331968.

%t lst = {}; Do[s = ToString@n; d = ToString@DivisorSigma[1, n]; If[StringLength@d == StringLength@d && {}!= StringPosition[s<>s, d], AppendTo[lst, n]], {n, 10^6}]; lst

%Y Cf. A000203.

%K base,nonn,more

%O 1,2

%A _Giovanni Resta_, Jan 26 2006