A363326 Total number of parts coprime to n in the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 8, 8, 14, 24, 29, 56, 63, 104, 118, 232, 166, 416, 327, 564, 567, 1168, 656, 1700, 1357, 2186, 1904, 4200, 1695, 6112, 4206, 6431, 5844, 10167, 5597, 16832, 10935, 16560, 12281, 30624, 11444, 40528, 24370, 32311, 32908, 68704, 28835, 81129, 44289, 79444, 65437

Offset

1,8

Links

Table of n, a(n) for n=1..52.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} (c(i) + c(j) + c(k) + c(l) + c(m) + c(o) + c(p) + c(n-i-j-k-l-m-o-p)), where c(x) = [gcd(n,x) = 1] and [ ] is the Iverson bracket.

Example

The partitions of 11 into 8 parts are: 1+1+1+1+1+1+1+4, 1+1+1+1+1+1+2+3, and 1+1+1+1+1+2+2+2. 11 is coprime to parts 1, 2, 3 and 4. Since there are 24 total parts in these partitions that are coprime to 11, a(11) = 24.

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), A363324 (k=6), A363325 (k=7), this sequence (k=8), A363327 (k=9), A363328 (k=10).

Sequence in context: A259532 A329822 A226835 * A343526 A335896 A168337

Adjacent sequences: A363323 A363324 A363325 * A363327 A363328 A363329

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 27 2023

Status

approved