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A338021
Number of partitions of n into two parts (s,t) such that s <= t and t | s*n.
7
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
OFFSET
1,6
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}]
PROG
(PARI) A338021(n) = sum(s=1, n\2, !((s*n)%(n-s))); \\ Antti Karttunen, Dec 12 2021
CROSSREFS
Cf. also A337101, A338117.
Sequence in context: A323879 A129308 A159200 * A318721 A219201 A341979
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Oct 06 2020
EXTENSIONS
Data section extended up to 105 terms by Antti Karttunen, Dec 12 2021
STATUS
approved