

A316561


Squarefree numbers whose arithmetic mean of digits is 4.


1



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
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OFFSET

1,1


LINKS



EXAMPLE

26 = 2*13 is a 2digit squarefree number whose arithmetic mean of digits is (2 + 6)/2 = 4. Hence, 26 is a term.
165 = 3 * 5 * 11 is a 3digit 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:


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



KEYWORD

nonn,base


AUTHOR



STATUS

approved



