A116910 Numbers k such that the number of letters in the Roman numeral for k divides k.

1, 2, 3, 4, 5, 6, 8, 10, 12, 20, 21, 24, 30, 40, 44, 45, 48, 50, 54, 60, 64, 80, 84, 85, 88, 90, 92, 96, 100, 102, 110, 111, 112, 116, 120, 132, 133, 135, 150, 152, 156, 168, 174, 175, 180, 182, 189, 200, 201, 204, 210, 220, 222, 225, 230, 240, 245, 246, 248

Offset: 1

Author

Jonathan Vos Post, Mar 17 2006

Keywords

• base
• easy
• nonn
• less

Examples

			a(23) = 84 because there are 6 letters in LXXXIV and 6 divides 84.
a(44) = 189 because there are 7 letters in CLXXXIX and 7 divides 189.
a(56) = 248 because there are 8 letters in CCXLVIII and 8 divides 248.
		

Links

• Nathaniel Johnston and Harvey P. Dale, Table of n, a(n) for n = 1..1000 (first 593 terms from Nathaniel Johnston)

Crossrefs

Cf. A006968.

Programs

Maple

for n from 1 to 500 do if(n mod length(convert(n,roman)) = 0)then printf("%d, ",n): fi: od: # Nathaniel Johnston, May 18 2011

Mathematica

Select[Range[250],Divisible[#,StringLength[IntegerString[#,"Roman"]]]&] (* Harvey P. Dale, Feb 13 2013 *)

Formula

{k such that A006968(k)|k}.

Extensions

Corrected by Nathaniel Johnston, May 18 2011