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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A286305 Number of partitions of n into powerful parts (A001694). 1
1, 1, 1, 1, 2, 2, 2, 2, 4, 5, 5, 5, 7, 8, 8, 8, 12, 14, 15, 15, 19, 21, 22, 22, 28, 33, 35, 37, 43, 48, 50, 52, 62, 70, 75, 79, 92, 100, 105, 109, 126, 140, 148, 157, 177, 194, 202, 211, 237, 261, 276, 290, 324, 351, 370, 384, 424, 462, 489, 514, 562, 609, 640, 670, 728, 787, 831, 873, 948, 1016, 1071, 1118, 1210, 1296, 1366, 1433 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..75.

Eric Weisstein's World of Mathematics, Powerful Number

Index entries for sequences related to powerful numbers

Index entries for sequences related to partitions

FORMULA

G.f.: Product_{k>=1} 1/(1 - x^A001694(k)).

a(n) = A078635(n) for n < 72.

EXAMPLE

a(8) = 4 because we have [8], [4, 4], [4, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1].

MATHEMATICA

nmax = 75; CoefficientList[Series[1/(1 - x) Product[1/(1 - Boole[Min@ FactorInteger[k][[All, 2]] > 1] x^k), {k, 2, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A001694, A078635, A286320.

Sequence in context: A029078 A131799 A078635 * A046768 A274151 A216393

Adjacent sequences:  A286302 A286303 A286304 * A286306 A286307 A286308

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 12 2017

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 20 02:03 EDT 2019. Contains 328244 sequences. (Running on oeis4.)