

A281957


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


1



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
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OFFSET

1,3


LINKS

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


EXAMPLE


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.


PROG

(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;


CROSSREFS

Cf. A000070, A008284, A052810.
Sequence in context: A213855 A272206 A122797 * A286389 A309945 A103354
Adjacent sequences: A281954 A281955 A281956 * A281958 A281959 A281960


KEYWORD

nonn,easy


AUTHOR

Arkadiusz Wesolowski, Feb 03 2017


STATUS

approved



