A164817 - OEIS

A164817

Positive numbers n with property that average digit of n^2 is 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

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OFFSET

1,2

COMMENTS

A004159(n)/nod(n^2) = sod(n^2)/nod(n^2) is 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

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 *)

PROG

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