A363323 - OEIS

%I #5 May 27 2023 23:25:02

%S 0,0,0,0,5,4,10,10,22,19,50,28,90,63,102,104,235,108,350,192,343,313,

%T 705,301,831,576,919,684,1665,515,2135,1274,1813,1555,2540,1324,4155,

%U 2360,3397,2359,6130,1953,7345,3858,4925,4854,10310,3890,10790,5457,9421,7351,16330,6077

%N Total number of parts coprime to n in the partitions of n into 5 parts.

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

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

%e The partitions of 9 into 5 parts are: 1+1+1+1+5, 1+1+1+2+4, 1+1+1+3+3, 1+1+2+2+3, and 1+2+2+2+2. 9 is relatively prime to 1, 2, 4 and 5. Since there are 22 total parts in these partitions that are coprime to 9, a(9) = 22.

%Y For similar sequences into k parts for k = 2..10, see: A000010(n>2) (k=2), A363278 (k=3), A363322 (k=4), this sequence (k=5), A363324 (k=6), A363325 (k=7), A363326 (k=8), A363327 (k=9), A363328 (k=10).

%K nonn,easy

%O 1,5

%A _Wesley Ivan Hurt_, May 27 2023