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%I #29 Apr 18 2022 22:51:12
%S 1,2,3,4,5,12,7,8,18,10,11,24,13,14,45,16,17,36,19,40,42,22,23,48,50,
%T 26,54,56,29,90,31,32,66,34,105,72,37,38,78,80,41,126,43,44,180,46,47,
%U 96,98,100,102,52,53,162,110,112,114,58,59,180,61,62,252,64,130,198
%N Sum of all parts of all partitions of n into an odd number of consecutive parts.
%C a(n) is n times the number of partitions of n into an odd number of consecutive parts.
%F a(n) = n*A082647(n).
%F a(n) = A245579(n) - A352505(n). - _Omar E. Pol_, Mar 19 2022
%e For n = 15 the partitions of 15 into an odd number of consecutive parts are [15], [6, 5, 4] and [5, 4, 3, 2, 1], so a(15) = 15 + 6 + 5 + 4 + 5 + 4 + 3 + 2 + 1 = 15*3 = 45.
%o (PARI) a(n) = my(q = sqrt(2*n)); n*sumdiv(n, d, (d%2) && (d < q)); \\ _Michel Marcus_, Mar 11 2022; after A082647
%Y Row sums of A352499.
%Y Cf. A066186, A082647, A237048, A245579, A286000, A286001, A299765, A351824, A352505.
%K nonn
%O 1,2
%A _Omar E. Pol_, Mar 09 2022