A363322 Total number of parts coprime to n in the partitions of n into 4 parts.

0, 0, 0, 4, 4, 5, 12, 12, 19, 20, 44, 23, 72, 48, 67, 76, 156, 70, 216, 112, 182, 172, 376, 155, 408, 276, 422, 310, 740, 226, 900, 524, 697, 600, 936, 490, 1512, 828, 1144, 800, 2044, 644, 2352, 1198, 1488, 1448, 3056, 1125, 3053, 1524, 2539, 1976, 4356, 1586, 3672, 2272

Offset

1,4

Links

Table of n, a(n) for n=1..56.

Index entries for sequences related to partitions

Formula

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

Example

The partitions of 8 into 4 parts are: 1+1+1+5, 1+1+2+4, 1+1+3+3, 1+2+2+3, and 2+2+2+2. 8 is relatively prime to 1, 3, and 5. Since there are 12 total parts in these partitions that are coprime to 8, a(8) = 12.

Crossrefs

For similar sequences into k parts for k = 2..10, see: A000010(n>2) (k=2), A363278 (k=3), this sequence (k=4), A363323 (k=5), A363324 (k=6), A363325 (k=7), A363326 (k=8), A363327 (k=9), A363328 (k=10).

Sequence in context: A107851 A302337 A098821 * A142154 A084458 A248933

Adjacent sequences: A363319 A363320 A363321 * A363323 A363324 A363325

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 27 2023

Status

approved