A363325 Total number of parts coprime to n in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 7, 6, 13, 16, 35, 30, 77, 65, 118, 122, 266, 156, 455, 308, 551, 529, 1148, 571, 1573, 1182, 1924, 1585, 3654, 1310, 5131, 3344, 5056, 4494, 7715, 4133, 12768, 7923, 11875, 8549, 21840, 7636, 28077, 16126, 21110, 21381, 45010, 18177, 51225, 27170

Offset

1,7

Links

Table of n, a(n) for n=1..50.

Index entries for sequences related to partitions

Formula

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.

Example

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.

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

Sequence in context: A215338 A176414 A297153 * A259168 A309624 A078323

Adjacent sequences: A363322 A363323 A363324 * A363326 A363327 A363328

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 27 2023

Status

approved