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A340284 Number of partitions of n into 3 parts such that the 'middle' part is relatively prime to each of the other two parts. 2
0, 0, 1, 1, 1, 2, 1, 3, 3, 4, 2, 7, 4, 9, 7, 9, 7, 15, 9, 18, 14, 19, 12, 27, 15, 26, 21, 30, 21, 44, 25, 43, 35, 46, 34, 58, 34, 59, 46, 64, 43, 82, 47, 80, 64, 83, 58, 107, 65, 106, 79, 110, 75, 137, 86, 128, 98, 132, 92, 172, 96, 155, 122, 161, 118, 198, 119, 188, 147 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..69.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} floor(1/gcd(i,k)) * floor(1/gcd(i,n-i-k)).

MATHEMATICA

Table[Sum[Sum[Floor[1/GCD[i, k]]*Floor[1/GCD[i, n - i - k]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 80}]

CROSSREFS

Cf. A340283, A340285.

Sequence in context: A082666 A057938 A144623 * A218975 A048619 A116087

Adjacent sequences:  A340281 A340282 A340283 * A340285 A340286 A340287

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jan 02 2021

STATUS

approved

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Last modified January 23 14:31 EST 2022. Contains 350512 sequences. (Running on oeis4.)