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A340756 Number of partitions of n into 4 semiprime parts. 3
1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 3, 3, 4, 2, 3, 4, 5, 6, 5, 4, 7, 7, 9, 9, 9, 7, 9, 12, 13, 11, 11, 13, 16, 17, 17, 18, 18, 17, 20, 25, 25, 23, 24, 26, 32, 29, 31, 33, 31, 33, 35, 43, 43, 40, 39, 45, 48, 52, 50, 52, 53, 52, 61, 69, 67, 61, 61, 70, 79, 76, 76, 80, 81, 85, 88, 101 (list; graph; refs; listen; history; text; internal format)
OFFSET

16,7

LINKS

Alois P. Heinz, Table of n, a(n) for n = 16..10000

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) = 2], where Omega is the number of prime factors with multiplicity (A001222) and [ ] is the (generalized) Iverson bracket.

a(n) = [x^n y^4] 1/Product_{j>=1} (1-y*x^A001358(j)). - Alois P. Heinz, May 21 2021

MATHEMATICA

Table[Sum[Sum[Sum[KroneckerDelta[PrimeOmega[k], PrimeOmega[j], PrimeOmega[i], PrimeOmega[n - i - j - k], 2], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 16, 100}]

CROSSREFS

Cf. A001222 (Omega), A001358.

Column k=4 of A344447.

Sequence in context: A029334 A275078 A286478 * A030273 A029197 A029174

Adjacent sequences:  A340753 A340754 A340755 * A340757 A340758 A340759

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jan 19 2021

STATUS

approved

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Last modified November 29 13:17 EST 2021. Contains 349416 sequences. (Running on oeis4.)