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

1,2

Links

Table of n, a(n) for n=1..64.

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).

Formula

a(n) = n + 47 for n > 30. - Charles R Greathouse IV, Jun 19 2024

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 *)

Crossrefs

Cf. A051882, A028229.

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

Sequence in context: A091805 A229057 A086710 * A051909 A372582 A112134

Adjacent sequences: A052425 A052426 A052427 * A052429 A052430 A052431

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved