A281957 - OEIS

%I #15 Sep 08 2022 08:46:18

%S 1,1,2,2,3,4,4,5,6,7,7,8,9,10,11,12,12,13,14,15,16,17,18,19,19,20,21,

%T 22,23,24,25,26,27,28,29,30,30,31,32,33,34,35,36,37,38,39,40,41,42,43,

%U 44,45,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61

%N a(n) = largest k such that n has at least k partitions each containing at least k parts.

%H Alois P. Heinz, <a href="/A281957/b281957.txt">Table of n, a(n) for n = 1..20000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition</a>

%e -------------------------------------

%e                           Number

%e Partitions of 5          of terms

%e -------------------------------------

%e 5 .......................... 1

%e 1 + 4 ...................... 2

%e 2 + 3 ...................... 2

%e 1 + 1 + 3 .................. 3

%e 1 + 2 + 2 .................. 3

%e 1 + 1 + 1 + 2 .............. 4

%e 1 + 1 + 1 + 1 + 1 .......... 5

%e -------------------------------------

%e There are 7 partitions of the integer 5 is 7. The four partitions 1 + 1 + 3, 1 + 2 + 2, 1 + 1 + 1 + 2 and 1 + 1 + 1 + 1 + 1 each have at least 3 parts, so a(5) = 3.

%o (Magma) lst:=[]; k:=1; s:=0; for m in [0..8] do s+:=NumberOfPartitions(m); while k le s do Append(~lst, k); k+:=1; end while; Append(~lst, s); end for; lst;

%Y Cf. A000070, A008284, A052810.

%K nonn,easy

%O 1,3

%A _Arkadiusz Wesolowski_, Feb 03 2017