A316561 Squarefree numbers whose arithmetic mean of digits is 4.

17, 26, 35, 53, 62, 71, 129, 138, 165, 174, 183, 219, 237, 246, 255, 273, 282, 291, 309, 318, 327, 345, 354, 381, 390, 417, 426, 435, 453, 462, 471, 534, 543, 561, 570, 606, 615, 633, 642, 651, 705, 714, 723, 741, 813, 822, 831, 903, 921, 930, 1069, 1087, 1159

Offset: 1

Author

K. D. Bajpai, Jul 06 2018

Keywords

• nonn
• base

Examples

			26 = 2*13 is a 2-digit squarefree number whose arithmetic mean of digits is (2 + 6)/2 = 4. Hence, 26 is a term.
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.
		

Links

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

Crossrefs

Intersection of A005117 (squarefree numbers) and A061387.

Cf. A316484.

Programs

Magma

[k:k in [4..1200]| IsSquarefree(k) and &+Intseq(k) eq 4*#Intseq(k)]; // Marius A. Burtea, Dec 19 2019

Maple

filter:= proc(n) local L;
  if not numtheory:-issqrfree(n) then return false fi;
  L:= convert(n,base,10);
  convert(L,`+`)=4*nops(L)
end proc:
select(filter, [$1..1000]); # Robert Israel, Jul 06 2018

Mathematica

Select[Range[5000], Mean[IntegerDigits[#]] == 4 && SquareFreeQ[#] &]