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A281957 a(n) = largest k such that n has at least k partitions each containing at least k parts.

%I A281957 #15 Sep 08 2022 08:46:18
%S A281957 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 A281957 22,23,24,25,26,27,28,29,30,30,31,32,33,34,35,36,37,38,39,40,41,42,43,
%U A281957 44,45,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61
%N A281957 a(n) = largest k such that n has at least k partitions each containing at least k parts.
%H A281957 Alois P. Heinz, <a href="/A281957/b281957.txt">Table of n, a(n) for n = 1..20000</a>
%H A281957 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition</a>
%e A281957 -------------------------------------
%e A281957                           Number
%e A281957 Partitions of 5          of terms
%e A281957 -------------------------------------
%e A281957 5 .......................... 1
%e A281957 1 + 4 ...................... 2
%e A281957 2 + 3 ...................... 2
%e A281957 1 + 1 + 3 .................. 3
%e A281957 1 + 2 + 2 .................. 3
%e A281957 1 + 1 + 1 + 2 .............. 4
%e A281957 1 + 1 + 1 + 1 + 1 .......... 5
%e A281957 -------------------------------------
%e A281957 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 A281957 (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 A281957 Cf. A000070, A008284, A052810.
%K A281957 nonn,easy
%O A281957 1,3
%A A281957 _Arkadiusz Wesolowski_, Feb 03 2017