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Numbers n such that the number of letters in the Roman numeral for n divides n.
2

%I #24 Sep 03 2017 11:13:20

%S 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,

%T 90,92,96,100,102,110,111,112,116,120,132,133,135,150,152,156,168,174,

%U 175,180,182,189,200,201,204,210,220,222,225,230,240,245,246,248

%N Numbers n such that the number of letters in the Roman numeral for n divides n.

%H Nathaniel Johnston and Harvey P. Dale, <a href="/A116910/b116910.txt">Table of n, a(n) for n = 1..1000</a> (* first 593 terms from Nathaniel Johnston *)

%F {n such that A006968(n)|n}.

%e a(23) = 84 because there are 6 letters in LXXXIV and 6 divides 84.

%e a(44) = 189 because there are 7 letters in CLXXXIX and 7 divides 189.

%e a(56) = 248 because there are 8 letters in CCXLVIII and 8 divides 248.

%p 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

%t Select[Range[250],Divisible[#,StringLength[IntegerString[#,"Roman"]]]&] (* _Harvey P. Dale_, Feb 13 2013 *)

%Y Cf. A006968.

%K base,easy,nonn,less

%O 1,2

%A _Jonathan Vos Post_, Mar 17 2006

%E Corrected by _Nathaniel Johnston_, May 18 2011