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%I #6 Feb 05 2024 13:05:46
%S 0,1,0,1,0,2,1,2,1,2,1,3,1,3,1,3,2,4,2,5,3,5,3,5,4,6,4,7,3,6,3,6,5,9,
%T 5,9,5,8,4,9,6,10,7,12,7,10,7,11,9,13,8,14,8,12,8,13,11,15,11,17,12,
%U 16,11,15,12,17,13,18,12,16,14,18,16,20,15,21,14,17,15
%N Number of partitions of n into two arithmetic numbers.
%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 = A245656.
%e a(14) = 3 ways (13+1 = 11+3 = 7+7).
%t a[n_] := Boole[IntegerQ[Mean[Divisors[n]]]]; Table[Sum[a[k]*a[n - k], {k, Floor[n/2]}], {n, 100}]
%Y Cf. A003601, A245656, A369917 (distinct).
%K nonn,easy
%O 1,6
%A _Wesley Ivan Hurt_, Feb 05 2024