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

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, 22, 23, 24, 25, 26, 27, 28, 29, 30, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61

Offset: 1

Author

Arkadiusz Wesolowski, Feb 03 2017

Keywords

• nonn
• easy

Examples

			-------------------------------------
                          Number
Partitions of 5          of terms
-------------------------------------
5 .......................... 1
1 + 4 ...................... 2
2 + 3 ...................... 2
1 + 1 + 3 .................. 3
1 + 2 + 2 .................. 3
1 + 1 + 1 + 2 .............. 4
1 + 1 + 1 + 1 + 1 .......... 5
-------------------------------------
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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000
• Wikipedia, Partition

Crossrefs

Cf. A000070, A008284, A052810.

Programs

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;