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Number of ways to write n as the sum of 2 balanced numbers.
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%I #42 Feb 02 2022 23:37:52

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

%T 0,2,1,1,0,0,1,1,1,2,2,0,1,1,1,1,0,0,0,1,0,1,2,1,1,1,0,1,0,0,1,0,0,1,

%U 0,2,2,2,1,0,0,1,1,0,1,1,1,1,0,3,1,1,0,0,0,1,1,1,1

%N Number of ways to write n as the sum of 2 balanced numbers.

%C A balanced number k is a number such that phi(k) | sigma(k).

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

%F a(n) = Sum_{k=1..floor(n/2)} c(k) * c(n-k), where c = A351114.

%e a(84) = 3; 84 = 78+6 = 70+14 = 42+42.

%Y Cf. A020492 (balanced numbers), A351114.

%K nonn

%O 1,4

%A _Wesley Ivan Hurt_, Feb 01 2022