A052428 Strict Egyptian numbers (complement of A051882).
1, 11, 24, 30, 31, 32, 37, 38, 43, 45, 50, 52, 53, 54, 55, 57, 59, 60, 61, 62, 64, 65, 66, 67, 69, 71, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111
Offset: 1
Links
- Max A. Alekseyev, On partitions into squares of distinct integers whose reciprocals sum to 1, The Mathematics of Various Entertaining Subjects: Volume 3: The Magic of Mathematics, Part III Algebra and Number Theory (2019), 213-221.
- R. L. Graham, A theorem on partitions, J. Austral. Math. Soc. 3:4 (1963), pp. 435-441.
- Eric Weisstein's World of Mathematics, Egyptian Number.
- Index entries for sequences related to Egyptian fractions
- Index entries for linear recurrences with constant coefficients, signature (2,-1).
Programs
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Mathematica
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 *)
Formula
a(n) = n + 47 for n > 30. - Charles R Greathouse IV, Jun 19 2024