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A333496 Least k of Egyptian fractions 1 = 1/x_1 + ... + 1/x_k , with 0 < x_1 <= ... <= x_k = n.

%I A333496 #29 Mar 24 2020 22:30:35
%S A333496 1,2,3,3,5,3,7,4,5,4,11,4,13,5,4,5,17,4,19,4,5,7,23,4,8,8,6,5,29,5,31,
%T A333496 6,5,10,5,5,37
%N A333496 Least k of Egyptian fractions 1 = 1/x_1 + ... + 1/x_k , with 0 < x_1 <= ... <= x_k = n.
%H A333496 <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%F A333496 a(n) <= n.
%F A333496 a(m * n) <= a(n) + m - 1.
%F A333496 If p is prime, a(p) = p.
%F A333496 If m is odd, a(2 * m) <= (m - 1)/2 + 2 because 1 = 1/2 + (m - 1)/2 * 1/m + 1/(2 * m).
%e A333496 One of solutions
%e A333496   n  |  [x_1, x_2, ... , x_a(n)]
%e A333496 -----+--------------------------------------
%e A333496    4 | [2,  4,  4]
%e A333496    6 | [2,  3,  6]
%e A333496    8 | [2,  4,  8,  8]
%e A333496    9 | [2,  6,  9,  9,  9]
%e A333496   10 | [2,  5,  5, 10]
%e A333496   12 | [2,  3, 12, 12]
%e A333496   14 | [2,  7,  7,  7, 14]
%e A333496   15 | [2,  3, 10, 15]
%e A333496   16 | [2,  4,  8, 16, 16]
%e A333496   18 | [2,  3,  9, 18]
%e A333496   20 | [2,  4,  5, 20]
%e A333496   21 | [2,  3, 14, 21, 21]
%e A333496   22 | [2, 11, 11, 11, 11, 11, 22]
%e A333496   24 | [2,  3,  8, 24]
%e A333496   25 | [2,  4, 20, 25, 25, 25, 25, 25]
%e A333496   26 | [2, 13, 13, 13, 13, 13, 13, 26]
%e A333496   27 | [2,  3, 18, 27, 27, 27]
%e A333496   28 | [2,  3, 12, 21, 28]
%e A333496   30 | [2,  3, 10, 30, 30]
%e A333496   32 | [2,  3, 16, 24, 32, 32]
%e A333496   33 | [2,  3, 11, 22, 33]
%e A333496   34 | [2, 17, 17, 17, 17, 17, 17, 17, 17, 34]
%e A333496   35 | [2,  3, 14, 15, 35]
%e A333496   36 | [2,  3,  9, 36, 36]
%Y A333496 Cf. A020473, A092666, A333437.
%K A333496 nonn,more
%O A333496 1,2
%A A333496 _Seiichi Manyama_, Mar 24 2020