A363326 - OEIS

%I #5 May 27 2023 23:23:13

%S 0,0,0,0,0,0,0,8,8,14,24,29,56,63,104,118,232,166,416,327,564,567,

%T 1168,656,1700,1357,2186,1904,4200,1695,6112,4206,6431,5844,10167,

%U 5597,16832,10935,16560,12281,30624,11444,40528,24370,32311,32908,68704,28835,81129,44289,79444,65437

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

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F 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.

%e 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.

%Y 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).

%K nonn,easy

%O 1,8

%A _Wesley Ivan Hurt_, May 27 2023