A338021 - OEIS

A338021

Number of partitions of n into two parts (s,t) such that s <= t and t | s*n.

0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 3, 0, 1, 1, 1, 0, 2, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 4, 0, 1, 0, 1, 1, 3, 0, 1, 0, 3, 0, 3, 0, 1, 2, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 3, 0, 1, 0, 6, 0, 1, 1, 1, 0, 3, 0, 1, 0, 3, 0, 4, 0, 1, 1, 1, 1, 2, 0, 3, 0, 1, 0, 6, 0, 1, 0, 2, 0, 6, 1, 1, 0, 1, 0, 3, 0, 1, 1, 2, 0, 2, 0, 2, 2

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OFFSET

1,6

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to partitions

FORMULA

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

EXAMPLE

a(6) = 2; The partitions of 6 into 2 parts are (1,5), (2,4) and (3,3). Since 4 | 2*6 = 12 and 3 | 3*6 = 18, we have two such partitions.

MATHEMATICA

Table[Sum[(1 - Ceiling[n*i/(n - i)] + Floor[n*i/(n - i)]), {i, Floor[n/2]}], {n, 100}]