cp's OEIS Frontend

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

%I A131998 #11 Mar 03 2025 09:34:29
%S A131998 5,7,10,24,33,40,44,70,78,84,90,99,105,126,132,168,176,189,190,198,
%T A131998 208,210,231,252,306,315,340,360,368,384,391,408,420,441,462,480,520,
%U A131998 546,575,580,598,600,608,612,638,682,693,700,702,736,740,760,770,792,814
%N A131998 Numbers m such that the number of letters in the m-th ordinal number divides m.
%C A131998 Which numbers k occur as the dividends?
%C A131998   k   smallest n such that A006944(n)/n = k
%C A131998   1   5
%C A131998   2  10
%C A131998   3  11
%C A131998   4  44
%C A131998   5  never?
%C A131998   6  78
%C A131998   7  70
%C A131998   8 168
%C A131998   9 189
%C A131998  10  90
%C A131998  11  99
%F A131998 {n such that A006944(n)|n}.
%e A131998 a(1) = 5 because "fifth" has 5 letters.
%e A131998 a(2) = 7 because "seventh" has 7 letters.
%e A131998 a(3) = 10 because "tenth" has 5 letters and 10/5 = 2.
%e A131998 a(4) = 24 because "twentyfourth" has 12 letters and 24/12 = 2.
%e A131998 a(5) = 33 because "thirtythird" has 11 letters and 33/11 = 3.
%e A131998 a(6) = 44 because "fortyfourth" has 11 letters and 44/11 = 4.
%t A131998 Select[Range[814],Divisible[#,Length[Select[Characters[IntegerName[#,"Ordinal"]],LetterQ]]]&] (* _James C. McMahon_, Mar 02 2025 *)
%Y A131998 Cf. A006944, A116910.
%K A131998 easy,nonn,word
%O A131998 1,1
%A A131998 _Jonathan Vos Post_, Oct 08 2007
%E A131998 Corrected and extended by _R. J. Mathar_, Oct 24 2007