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

1,1

Links

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

Example

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.

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[#] &]

Prog

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

Crossrefs

Intersection of A005117 (squarefree numbers) and A061387.

Cf. A316484.

Sequence in context: A212909 A273785 A171169 * A034963 A120143 A031204

Adjacent sequences: A316558 A316559 A316560 * A316562 A316563 A316564

Keyword

nonn,base

Author

K. D. Bajpai, Jul 06 2018

Status

approved