A363278 - OEIS

%I #9 May 27 2023 23:25:46

%S 0,0,3,2,6,3,12,8,15,10,30,12,42,21,32,32,72,27,90,40,66,55,132,48,

%T 130,78,126,84,210,60,240,128,170,136,216,108,342,171,240,160,420,126,

%U 462,220,276,253,552,192,525,250,416,312,702,243,560,336,522,406,870,240,930,465

%N Total number of parts coprime to n in the partitions of n into 3 parts.

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

%F a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} ([gcd(n,n-i-j) = 1] + [gcd(n,i) = 1] + [gcd(n,j) = 1]), where [ ] is the Iverson Bracket.

%e The partitions of 5 into 3 parts are: 3+1+1 and 2+2+1. 5 is coprime to 1, 2 and 3. Since there are 6 total parts in the partitions of 5 that are coprime to 5, a(5) = 6.

%t Table[Sum[Sum[KroneckerDelta[GCD[n, n - i - j], 1] + KroneckerDelta[GCD[n, j], 1] + KroneckerDelta[GCD[n, i], 1], {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 100}]

%Y For similar sequences into k parts for k = 2..10, see: A000010(n>2) (k=2), this sequence (k=3), A363322 (k=4), A363323 (k=5), A363324 (k=6), A363325 (k=7), A363326 (k=8), A363327 (k=9), A363328 (k=10).

%K nonn,easy

%O 1,3

%A _Wesley Ivan Hurt_, May 25 2023