login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A280195 Expansion of 1/(1 - Sum_{k>=2} floor(1/omega(k))*x^k), where omega(k) is the number of distinct prime factors (A001221). 8
1, 0, 1, 1, 2, 3, 4, 8, 11, 19, 28, 47, 72, 116, 182, 289, 460, 724, 1153, 1820, 2891, 4572, 7249, 11482, 18190, 28821, 45651, 72338, 114582, 181549, 287596, 455647, 721847, 1143588, 1811748, 2870239, 4547232, 7203907, 11412882, 18080833, 28644680, 45380392, 71894054, 113898439, 180443915, 285869028, 452888824, 717490903, 1136687237 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Number of compositions (ordered partitions) into prime powers (1 excluded).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Prime Power

Index entries for sequences related to compositions

FORMULA

G.f.: 1/(1 - Sum_{k>=2} floor(1/omega(k))*x^k).

EXAMPLE

a(6) = 4 because we have [4, 2], [3, 3], [2, 4] and [2, 2, 2].

MATHEMATICA

nmax = 48; CoefficientList[Series[1/(1 - Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]

CROSSREFS

Cf. A001221, A023360, A023894, A246655.

Sequence in context: A135909 A046812 A269797 * A286224 A245388 A164573

Adjacent sequences:  A280192 A280193 A280194 * A280196 A280197 A280198

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 28 2016

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 March 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)