A363325 - OEIS

%I #6 May 27 2023 23:24:04

%S 0,0,0,0,0,0,7,6,13,16,35,30,77,65,118,122,266,156,455,308,551,529,

%T 1148,571,1573,1182,1924,1585,3654,1310,5131,3344,5056,4494,7715,4133,

%U 12768,7923,11875,8549,21840,7636,28077,16126,21110,21381,45010,18177,51225,27170

%N Total number of parts coprime to n in the partitions of n into 7 parts.

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

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

%e The partitions of 10 into 7 parts are: 1+1+1+1+1+1+4, 1+1+1+1+1+2+3, and 1+1+1+1+2+2+2. 10 is coprime to 1 and 3. Since there are 16 total parts in these partitions that are coprime to 10, a(10) = 16.

%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), this sequence (k=7), A363326 (k=8), A363327 (k=9), A363328 (k=10).

%K nonn,easy

%O 1,7

%A _Wesley Ivan Hurt_, May 27 2023