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A377853 Sum over all multiplicative partitions mu of n whose sum is also n (with factors >= 1), of the encoding as Product_{j in mu} prime(j).

%I A377853 #13 Nov 20 2024 05:18:46
%S A377853 2,3,5,16,11,43,17,211,223,293,31,3221,41,1675,7087,53109,59,118973,
%T A377853 67,382791,174153,47695,83,12164185,3965025,252005,36536423,36180075,
%U A377853 109,268148849,127,2749874307,81264777,5800075,1568669845,39708983447,157,26345635,1719664807
%N A377853 Sum over all multiplicative partitions mu of n whose sum is also n (with factors >= 1), of the encoding as Product_{j in mu} prime(j).
%H A377853 Alois P. Heinz, <a href="/A377853/b377853.txt">Table of n, a(n) for n = 1..3333</a>
%F A377853 a(prime(n)) = a(A000040(n)) = A006450(n).
%e A377853 The multiplicative partitions of n=8 whose sum is also n are {[8], [4,2,1,1], [2,2,2,1,1]}, encodings give {prime(8), prime(4)*prime(2)*prime(1)^2, prime(2)^3*prime(1)^2} = {19, 7*3*2^2, 3^3*2^2} = {19, 84, 108}, the sum gives 211.
%Y A377853 Row sums of A377852.
%Y A377853 Cf. A000040, A006450, A378176.
%K A377853 nonn
%O A377853 1,1
%A A377853 _Alois P. Heinz_, Nov 09 2024