A164817 Positive numbers n with property that average digit of n^2 is an integer.

1, 2, 3, 8, 12, 15, 18, 21, 24, 27, 30, 41, 58, 59, 68, 85, 95, 113, 122, 145, 152, 157, 158, 166, 176, 179, 184, 190, 193, 194, 212, 221, 238, 251, 256, 257, 266, 274, 275, 283, 284, 292, 311, 313, 330, 339, 345, 354, 360, 369, 375, 381, 387, 399, 402, 405, 417

Offset: 1

Author

Zak Seidov, Aug 27 2009

Keywords

• base
• nonn

Comments

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.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004159, A164818.

Programs

Maple

filter:= proc(n) local L;
L:= convert(n^2,base,10);
type(convert(L,`+`)/nops(L), integer)
end proc:
select(filter, [$1..1000]); # Robert Israel, Feb 24 2016

Mathematica

Select[Range[500],IntegerQ[Mean[IntegerDigits[#^2]]]&] (* Harvey P. Dale, May 25 2011 *)

PARI

isok(n) = my(d=digits(n^2)); (vecsum(d) % #d) == 0; \\ Michel Marcus, Feb 24 2016