A052428 - OEIS

%I #26 Feb 16 2025 08:32:42

%S 1,11,24,30,31,32,37,38,43,45,50,52,53,54,55,57,59,60,61,62,64,65,66,

%T 67,69,71,73,74,75,76,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,

%U 94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111

%N Strict Egyptian numbers (complement of A051882).

%H Max A. Alekseyev, <a href="https://doi.org/10.2307/j.ctvd58spj.18">On partitions into squares of distinct integers whose reciprocals sum to 1</a>, The Mathematics of Various Entertaining Subjects: Volume 3: The Magic of Mathematics, Part III Algebra and Number Theory (2019), 213-221.

%H R. L. Graham, <a href="https://doi.org/10.1017/S1446788700039045">A theorem on partitions</a>, J. Austral. Math. Soc. 3:4 (1963), pp. 435-441.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EgyptianNumber.html">Egyptian Number.</a>

%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = n + 47 for n > 30. - _Charles R Greathouse IV_, Jun 19 2024

%t strictEgyptianQ[m_]:=!Length[Select[IntegerPartitions[m, Ceiling[(Sqrt[8 m + 1] - 1) / 2]], Length[#]==Length[Union[#]]&&1==Plus@@(1/#)&, 1]]>0; Reap[Do[If[!strictEgyptianQ[m], Print[m]; Sow[m]], {m, 1,100}]][[2, 1]] (* _Vincenzo Librandi_, Jul 16 2017 *)

%Y Cf. A051882, A028229.

%Y Note that A051909 is a subset (but is strictly different).

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_