A363328 Total number of parts coprime to n in the partitions of n into 10 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 10, 17, 30, 42, 64, 86, 150, 142, 300, 277, 471, 502, 970, 669, 1556, 1345, 2190, 2037, 4230, 2142, 6530, 4876, 7657, 7162, 12746, 7488, 21120, 14751, 22864, 17986, 42420, 18156, 58880, 38177, 52533, 53185, 109360, 49563, 137515, 79738

Offset

1,10

Links

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

Index entries for sequences related to partitions

Formula

a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} (c(i) + c(j) + c(k) + c(l) + c(m) + c(o) + c(p) + c(q) + c(r) + c(n-i-j-k-l-m-o-p-q-r)), where c(x) = [gcd(n,x) = 1] and [ ] is the Iverson bracket.

Example

The partitions of 13 into 10 parts are: 1+1+1+1+1+1+1+1+1+4, 1+1+1+1+1+1+1+1+2+3, and 1+1+1+1+1+1+1+2+2+2. 13 is coprime to 1, 2, 3, and 4. Since there are 30 total parts in these partitions that are coprime to 13, a(13) = 30.

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), A363325 (k=7), A363326 (k=8), A363327 (k=9), this sequence (k=10).

Sequence in context: A167427 A227437 A352314 * A047879 A344336 A168416

Adjacent sequences: A363325 A363326 A363327 * A363329 A363330 A363331

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 27 2023

Status

approved