A164817 - OEIS

%I #18 Jan 09 2025 02:13:39

%S 1,2,3,8,12,15,18,21,24,27,30,41,58,59,68,85,95,113,122,145,152,157,

%T 158,166,176,179,184,190,193,194,212,221,238,251,256,257,266,274,275,

%U 283,284,292,311,313,330,339,345,354,360,369,375,381,387,399,402,405,417

%N Positive numbers n with property that average digit of n^2 is an integer.

%C A004159(n)/nod(n^2) = sod(n^2)/nod(n^2) is an integer, where sod(n^2)= sum of digits of n^2, nod(n^2) = number of digits of n^2. Correspondent values of sod(n^2)/nod(n^2) in A164818.

%H Robert Israel, <a href="/A164817/b164817.txt">Table of n, a(n) for n = 1..10000</a>

%p filter:= proc(n) local L;

%p L:= convert(n^2,base,10);

%p type(convert(L,`+`)/nops(L), integer)

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Feb 24 2016

%t Select[Range[500],IntegerQ[Mean[IntegerDigits[#^2]]]&] (* _Harvey P. Dale_, May 25 2011 *)

%o (PARI) isok(n) = my(d=digits(n^2)); (vecsum(d) % #d) == 0; \\ _Michel Marcus_, Feb 24 2016

%Y Cf. A004159, A164818.

%K base,nonn

%O 1,2

%A _Zak Seidov_, Aug 27 2009