A131998 Numbers m such that the number of letters in the m-th ordinal number divides m.

5, 7, 10, 24, 33, 40, 44, 70, 78, 84, 90, 99, 105, 126, 132, 168, 176, 189, 190, 198, 208, 210, 231, 252, 306, 315, 340, 360, 368, 384, 391, 408, 420, 441, 462, 480, 520, 546, 575, 580, 598, 600, 608, 612, 638, 682, 693, 700, 702, 736, 740, 760, 770, 792, 814

Offset: 1

Author

Jonathan Vos Post, Oct 08 2007

Keywords

• easy
• nonn
• word

Comments

Which numbers k occur as the dividends?

k smallest n such that A006944(n)/n = k

1 5

2 10

3 11

4 44

5 never?

6 78

7 70

8 168

9 189

10 90

11 99

Examples

			a(1) = 5 because "fifth" has 5 letters.
a(2) = 7 because "seventh" has 7 letters.
a(3) = 10 because "tenth" has 5 letters and 10/5 = 2.
a(4) = 24 because "twentyfourth" has 12 letters and 24/12 = 2.
a(5) = 33 because "thirtythird" has 11 letters and 33/11 = 3.
a(6) = 44 because "fortyfourth" has 11 letters and 44/11 = 4.
		

Crossrefs

Cf. A006944, A116910.

Programs

Mathematica

Select[Range[814],Divisible[#,Length[Select[Characters[IntegerName[#,"Ordinal"]],LetterQ]]]&] (* James C. McMahon, Mar 02 2025 *)

Formula

{n such that A006944(n)|n}.

Extensions

Corrected and extended by R. J. Mathar, Oct 24 2007