A113654 - OEIS

%I #8 Jul 22 2021 07:52:28

%S 1,11,101,125,153,1205,1502,1810,3080,7631,18010,18650,21020,36559,

%T 36911,44805,53999,60541,68443,120005,189585,210020,487195,1059449,

%U 1750004,1800010,1860050,1872250,2072139,2170100,2268661,2496750

%N Numbers k such that the square of k contains sigma(k) as a substring, in base 10.

%C If p = 180...01 is prime, then k = 2*5*p = 180...010, k^2 = 3240...0360...0100 and sigma(k) = 3240...036, thus k belongs to the sequence.

%e 153^2 = 23409 and sigma(153) = 234.

%t lst = {}; Do[If[{}!= StringPosition[ToString[n^2], ToString@DivisorSigma[1, n]], AppendTo[lst, n]], {n, 10^6}]; lst

%Y Cf. A000203, A000290.

%K base,nonn

%O 1,2

%A _Giovanni Resta_, Jan 26 2006