login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A340758 Number of partitions of n into 4 parts with the same number of distinct prime factors. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 21 17:37 EDT 2021. Contains 348155 sequences. (Running on oeis4.)