A182452 Numbers for which the sum of reciprocals of square of digits is an integer.

1, 11, 111, 1111, 2222, 11111, 12222, 21222, 22122, 22212, 22221, 111111, 112222, 121222, 122122, 122212, 122221, 211222, 212122, 212212, 212221, 221122, 221212, 221221, 222112, 222121, 222211, 222336, 222363, 222633, 223236, 223263, 223326, 223362, 223623

Offset: 1

Author

Michel Lagneau, Apr 29 2012

Keywords

• nonn
• base

Examples

			223623 is in the sequence because 1/2^2 + 1/2^2 + 1/3^2 + 1/6^2 + 1/2^2 + 1/3^2 = 1 is an integer.
		

Crossrefs

Cf. A034708.

Programs

Maple

T:=array(1..10):for n from 1 to 10^7 do:T:=convert(n,base,10):n1:=nops(T): s:=0:j:=0:for k from 1 to n1 do:if T[k]<>0 then s:=s+evalf(1/T[k]^2):else j:=1:fi: od: if j=0 and s=floor(s) then printf(`%d, `,n):else fi:od:

Mathematica

f[ n_ ] := 1/n^2; a[ n_ ] := Apply[ Plus, Map[ f, IntegerDigits[ n ] ] ] ; Select[ Range[ 1000 ], FreeQ[ IntegerDigits[ # ], 0 ] && IntegerQ[ a [ # ] ] & ]