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%I #8 Jan 08 2025 17:04:16
%S 1,11,111,1111,2222,11111,12222,21222,22122,22212,22221,111111,112222,
%T 121222,122122,122212,122221,211222,212122,212212,212221,221122,
%U 221212,221221,222112,222121,222211,222336,222363,222633,223236,223263,223326,223362,223623
%N Numbers for which the sum of reciprocals of square of digits is an integer.
%e 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.
%p 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:
%t f[ n_ ] := 1/n^2; a[ n_ ] := Apply[ Plus, Map[ f, IntegerDigits[ n ] ] ] ; Select[ Range[ 1000 ], FreeQ[ IntegerDigits[ # ], 0 ] && IntegerQ[ a [ # ] ] & ]
%Y Cf. A034708.
%K nonn,base
%O 1,2
%A _Michel Lagneau_, Apr 29 2012