A340758 Number of partitions of n into 4 parts with the same number of distinct prime factors.

0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, 13, 15, 18, 18, 22, 23, 27, 28, 32, 31, 38, 37, 41, 42, 49, 46, 53, 51, 62, 59, 70, 65, 82, 73, 89, 81, 99, 89, 108, 96, 118, 104, 128, 114, 142, 122, 153, 133, 167, 142, 178, 153, 195, 167, 207, 176, 225, 190, 243, 204

Offset

0,11

Links

Table of n, a(n) for n=0..67.

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)} [omega(k) = omega(j) = omega(i) = omega(n-i-j-k)], where omega is the number of distinct prime factors (A001221) and [ ] is the (generalized) Iverson bracket.

Mathematica

Table[Sum[Sum[Sum[KroneckerDelta[PrimeNu[k], PrimeNu[j], PrimeNu[i],  PrimeNu[n - i - j - k]], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 80}]

Crossrefs

Cf. A001221 (omega).

Sequence in context: A262525 A184105 A062469 * A238098 A328283 A034156

Adjacent sequences: A340755 A340756 A340757 * A340759 A340760 A340761

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 19 2021

Status

approved