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Write n as n = k1 + k2 + ... + km, so that all k are distinct positive integers and b = A001055(k1) + A001055(k2) + ... + A001055(km) becomes maximal. a(n) is the number of such partitions which attain this maximum.
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%I #18 Jan 11 2022 21:35:35

%S 1,1,1,2,1,2,1,1,3,1,2,5,2,3,1,2,3,1,2,4,1,2,5,1,2,5,1,2,5,1,2,5,1,2,

%T 4,1,1,3,7,1,3,6,1,2,5,1,1,4,1,1,3,1,11,2,4,9,2,3,7,1,2,4,7,1,3,6,1,2,

%U 4,1,1,3,1,1,2,1,6,1,2,4,1,1,3,3,1,1,1,5,5,1

%N Write n as n = k1 + k2 + ... + km, so that all k are distinct positive integers and b = A001055(k1) + A001055(k2) + ... + A001055(km) becomes maximal. a(n) is the number of such partitions which attain this maximum.

%F a(n) <= 1 + A066739(n) - A000041(n).

%e a(6) = 2:

%e 6 = 1 + 2 + 3 and A001055(1) + A001055(2) + A001055(3) = 3;

%e 6 = 2 + 4 and A001055(2) + A001055(4) = 3.

%Y Cf. A000009, A000041, A066739, A001055, A350029.

%K nonn

%O 1,4

%A _Thomas Scheuerle_, Dec 09 2021