A348537 Number of partitions of n into 3 parts whose largest part divides n.

0, 0, 1, 1, 0, 2, 0, 2, 1, 2, 0, 4, 0, 3, 1, 4, 0, 5, 0, 5, 1, 5, 0, 7, 0, 6, 1, 7, 0, 8, 0, 8, 1, 8, 0, 10, 0, 9, 1, 10, 0, 11, 0, 11, 1, 11, 0, 13, 0, 12, 1, 13, 0, 14, 0, 14, 1, 14, 0, 16, 0, 15, 1, 16, 0, 17, 0, 17, 1, 17, 0, 19, 0, 18, 1, 19, 0, 20, 0, 20, 1, 20, 0, 22, 0

Offset: 1

Author

Wesley Ivan Hurt, Oct 21 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10480
• Index entries for sequences related to partitions

Crossrefs

Cf. A069905.

Programs

Mathematica

Array[Sum[Sum[(1 - Ceiling[#/(# - i - j)] + Floor[#/(# - i - j)]), {i, j, Floor[(# - j)/2]} ], {j, Floor[#/3]} ] &, 85] (* Michael De Vlieger, Oct 21 2021 *)

PARI

A348537(n) = sum(j=1,(n\3), sum(i=j,((n-j)\2), (1 - ceil(n/(n-i-j)) + floor(n/(n-i-j))))); \\ Antti Karttunen, Feb 18 2023

Formula

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1 - ceiling(n/(n-i-j)) + floor(n/(n-i-j))).