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

1,1

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

Links

Table of n, a(n) for n=1..55.

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A006944, A116910.

Sequence in context: A356103 A339211 A088768 * A141443 A215660 A015849

Adjacent sequences: A131995 A131996 A131997 * A131999 A132000 A132001

Keyword

easy,nonn,word

Author

Jonathan Vos Post, Oct 08 2007

Extensions

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

Status

approved