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).

2, 3, 5, 16, 11, 43, 17, 211, 223, 293, 31, 3221, 41, 1675, 7087, 53109, 59, 118973, 67, 382791, 174153, 47695, 83, 12164185, 3965025, 252005, 36536423, 36180075, 109, 268148849, 127, 2749874307, 81264777, 5800075, 1568669845, 39708983447, 157, 26345635, 1719664807

Offset: 1

Author

Alois P. Heinz, Nov 09 2024

Keywords

• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..3333

Crossrefs

Row sums of A377852.

Cf. A000040, A006450, A378176.

Formula

a(prime(n)) = a(A000040(n)) = A006450(n).