A113654 Numbers k such that the square of k contains sigma(k) as a substring, in base 10.

1, 11, 101, 125, 153, 1205, 1502, 1810, 3080, 7631, 18010, 18650, 21020, 36559, 36911, 44805, 53999, 60541, 68443, 120005, 189585, 210020, 487195, 1059449, 1750004, 1800010, 1860050, 1872250, 2072139, 2170100, 2268661, 2496750

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..32.

Example

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

Mathematica

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

Crossrefs

Cf. A000203, A000290.

Sequence in context: A303570 A208262 A062696 * A066592 A316604 A208362

Adjacent sequences: A113651 A113652 A113653 * A113655 A113656 A113657

Keyword

base,nonn

Author

Giovanni Resta, Jan 26 2006

Status

approved