A286014 - OEIS

%I #21 Jul 21 2017 12:11:25

%S 1,2,4,4,7,7,10,8,15,11,16,15,19,16,27,16,25,26,28,22,38,26,34,31,40,

%T 31,50,29,43,49,46,32,62,41,59,48,55,46,74,46,61,67,64,46,94,56,70,63,

%U 77,69,98,55,79,85,92,61,110,71,88,93,91,76,131,64,110,103

%N Sum of smallest parts of all partitions of n into consecutive parts.

%C If n is a power of 2 then a(n) = n, the same as A286015(n).

%C Conjecture: this is also the row sums of A211343.

%H Alois P. Heinz, <a href="/A286014/b286014.txt">Table of n, a(n) for n = 1..10000</a>

%e For n = 15 there are four partitions of 15 into consecutive parts: [15], [8, 7], [6, 5, 4] and [5, 4, 3, 2, 1]. The sum of the smallest parts is 15 + 7 + 4 + 1 = 27, so a(15) = 27.

%t Table[Total[Select[IntegerPartitions@ n, Or[Length@ # == 1, Union@ Differences@ # == {-1}] &][[All, -1]]], {n, 66}] (* _Michael De Vlieger_, Jul 21 2017 *)

%Y Cf. A000079, A046746, A204217, A211343, A245579, A286015.

%K nonn

%O 1,2

%A _Omar E. Pol_, Apr 30 2017

%E More terms from _Alois P. Heinz_, May 01 2017