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A339627 Number of partitions of n into distinct parts such that the sum of reciprocals of parts is an integer. 2

%I #7 Dec 10 2020 16:46:56

%S 1,1,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,2,2,1,

%T 0,0,0,1,2,1,0,0,0,1,1,2,2,0,0,0,2,2,1,2,2,2,1,2,2,1,2,2,3,2,4,5,4,7,

%U 4,2,2,6,6,1,3,3,4,3,4

%N Number of partitions of n into distinct parts such that the sum of reciprocals of parts is an integer.

%C Also the number of ways to express an integer as the sum of distinct unit fractions such that the sum of the denominators is n.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

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

%e a(31) = 2 because we have 2 + 4 + 5 + 20 = 1 + 2 + 3 + 10 + 15 = 31 and 1/2 + 1/4 + 1/5 + 1/20 = 1, 1/1 + 1/2 + 1/3 + 1/10 + 1/15 = 2 are integers.

%Y Cf. A051907, A051908, A058360, A339628, A339629.

%K nonn

%O 0,32

%A _Ilya Gutkovskiy_, Dec 10 2020

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