login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A300982 Number of partitions of n into parts having the same number of prime divisors (counted with multiplicity) as n. 7

%I #10 Jul 09 2018 18:33:55

%S 1,1,1,1,1,2,1,3,1,1,2,6,1,9,3,2,1,17,1,23,2,4,7,40,1,7,10,1,3,87,2,

%T 111,1,17,25,21,1,219,34,34,2,336,4,413,7,2,73,614,1,87,7,103,10,1083,

%U 1,149,3,176,206,1850,2,2198,281,7,1,344,18,3630,25,479,22,5007,1,5861,725,13

%N Number of partitions of n into parts having the same number of prime divisors (counted with multiplicity) as n.

%H Alois P. Heinz, <a href="/A300982/b300982.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = [x^n] Product_{bigomega(k) = bigomega(n)} 1/(1 - x^k).

%e a(20) = 2 because we have [20] and [12, 8], where 20, 12 and 8 are numbers that are the product of exactly 3 (not necessarily distinct) primes.

%p with(numtheory):

%p a:= proc(m) option remember; local k, b; k, b:= bigomega(m),

%p proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p b(n, i-1)+`if`(bigomega(i)=k, b(n-i, min(i, n-i)), 0)))

%p end: b(m$2)

%p end:

%p seq(a(n), n=0..80); # _Alois P. Heinz_, Mar 17 2018

%t Table[SeriesCoefficient[Product[1/(1 - Boole[PrimeOmega[k] == PrimeOmega[n]] x^k), {k, 1, n}], {x, 0, n}], {n, 0, 75}]

%Y Cf. A001222, A300977, A300978, A300979, A300980, A300983.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Mar 17 2018

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)