Comments on A245579
Omar E. Pol

This file collects a number of comments added to A245579 by Omar E. Pol over the past several years - N. J. A. Sloane, Apr 27 2022

Sum of all parts of all partitions of n into consecutive parts. 

Sum of all parts of all partitions of n into an odd number of equal parts. 

Row sums of A299765. 

Row sums of A328362. 

Row sums of A285891 and of A328365. 

Number of partitions of n into consecutive parts, multiplied by n. Also, number of partitions of n into an odd number of equal parts, multiplied by n. 

For n = 10 there are two odd divisors of 10: 1 and 5, so a(10) = 2*10 = 20. On the other hand, for n = 10 there are two partitions of 10 into consecutive integers: [10] and [4, 3, 2, 1], and the sum of all parts of these partitions is 10 + 4 + 3 + 2 + 1 = 20, so a(10) = 20.

a(n) = n*A000005(n)/A001511(n) = A038040(n)/A001511(n). 

a(n) = A352257(n) + A352505(n).