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A356920 Number of partitions of n into 6 parts that divide n. 0
0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 8, 0, 1, 0, 4, 0, 8, 0, 8, 0, 0, 0, 33, 0, 0, 0, 6, 0, 27, 0, 5, 0, 0, 0, 44, 0, 0, 0, 21, 0, 16, 0, 1, 0, 0, 0, 61, 0, 3, 0, 1, 0, 13, 0, 11, 0, 0, 0, 124, 0, 0, 0, 5, 0, 6, 0, 0, 0, 8, 0, 104, 0, 0, 0, 0, 0, 5, 0, 31, 0, 0, 0, 77, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,10
LINKS
FORMULA
a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} c(n/m) * c(n/l) * c(n/k) * c(n/j) * c(n/i) * c(n/(n-i-j-k-l-m)), where c(n) = 1 - ceiling(n) + floor(n).
EXAMPLE
a(12) = 8; there are 8 ways to write 12 as the sum of 6 divisors of 12: 6+2+1+1+1+1 = 4+4+1+1+1+1 = 4+3+2+1+1+1 = 4+2+2+2+1+1 = 3+3+3+1+1+1 = 3+3+2+2+1+1 = 3+2+2+2+2+1 = 2+2+2+2+2+2.
CROSSREFS
Cf. A356609.
Sequence in context: A121814 A195298 A010581 * A276987 A348510 A200489
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Sep 04 2022
STATUS
approved

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Last modified April 20 04:18 EDT 2024. Contains 371798 sequences. (Running on oeis4.)