A363324 Total number of parts coprime to n in the partitions of n into 6 parts.

0, 0, 0, 0, 0, 6, 6, 10, 17, 21, 42, 34, 84, 74, 118, 128, 264, 146, 426, 272, 475, 458, 978, 463, 1250, 930, 1467, 1170, 2724, 913, 3672, 2324, 3382, 2989, 4949, 2643, 8160, 4904, 7153, 5079, 13032, 4355, 16212, 8964, 11514, 11617, 24420, 9581, 26701, 13888, 24347, 19392, 42624

Offset

1,6

Links

Table of n, a(n) for n=1..53.

Index entries for sequences related to partitions

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(i) + c(j) + c(k) + c(l) + c(m) + c(n-i-j-k-l-m)), where c(x) = [gcd(n,x) = 1] and [ ] is the Iverson bracket.

Example

The partitions of 9 into 6 parts are: 1+1+1+1+1+4, 1+1+1+1+2+3, and 1+1+1+2+2+2. 9 is relatively prime to 1, 2, and 4. Since there are 17 total parts in these partitions that are coprime to 9, a(9) = 17.

Crossrefs

For similar sequences into k parts for k = 2..10, see: A000010(n>2) (k=2), A363278 (k=3), A363322 (k=4), A363323 (k=5), this sequence (k=6), A363325 (k=7), A363326 (k=8), A363327 (k=9), A363328 (k=10).

Sequence in context: A366937 A096474 A220439 * A240620 A344328 A168282

Adjacent sequences: A363321 A363322 A363323 * A363325 A363326 A363327

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 27 2023

Status

approved