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A316561 Squarefree numbers whose arithmetic mean of digits is 4.

%I A316561 #23 Dec 27 2024 13:01:24
%S A316561 17,26,35,53,62,71,129,138,165,174,183,219,237,246,255,273,282,291,
%T A316561 309,318,327,345,354,381,390,417,426,435,453,462,471,534,543,561,570,
%U A316561 606,615,633,642,651,705,714,723,741,813,822,831,903,921,930,1069,1087,1159
%N A316561 Squarefree numbers whose arithmetic mean of digits is 4.
%H A316561 Robert Israel, <a href="/A316561/b316561.txt">Table of n, a(n) for n = 1..10000</a>
%e A316561 26 = 2*13 is a 2-digit squarefree number whose arithmetic mean of digits is (2 + 6)/2 = 4. Hence, 26 is a term.
%e A316561 165 = 3 * 5 * 11 is a 3-digit squarefree number whose arithmetic mean of digits is (1 + 6 + 5)/3 = 4. Hence, 165 is a term.
%p A316561 filter:= proc(n) local L;
%p A316561   if not numtheory:-issqrfree(n) then return false fi;
%p A316561   L:= convert(n,base,10);
%p A316561   convert(L,`+`)=4*nops(L)
%p A316561 end proc:
%p A316561 select(filter, [$1..1000]); # _Robert Israel_, Jul 06 2018
%t A316561 Select[Range[5000], Mean[IntegerDigits[#]] == 4 && SquareFreeQ[#] &]
%o A316561 (Magma) [k:k in [4..1200]| IsSquarefree(k) and &+Intseq(k) eq 4*#Intseq(k)]; // _Marius A. Burtea_, Dec 19 2019
%Y A316561 Intersection of A005117 (squarefree numbers) and A061387.
%Y A316561 Cf. A316484.
%K A316561 nonn,base
%O A316561 1,1
%A A316561 _K. D. Bajpai_, Jul 06 2018