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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A161148 Number of partitions of n such that each term of the partition is a squared divisor of n. 2
1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 5, 1, 4, 2, 6, 1, 9, 1, 8, 3, 6, 1, 16, 2, 7, 4, 12, 1, 21, 1, 15, 4, 9, 2, 39, 1, 10, 5, 25, 1, 35, 1, 24, 9, 12, 1, 76, 2, 21, 6, 32, 1, 61, 3, 38, 7, 15, 1, 174, 1, 16, 10, 46, 3, 93, 1, 50, 8, 42, 1, 231, 1, 19, 19, 60, 2, 135, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..79.

FORMULA

a(p)=1 if p a prime (A000040). a(2p)=A130291(n) if p=A000040(n). a(n) = [x^n] product_{d|n} 1/( 1-x^(d^2) ).

EXAMPLE

a(n=12)=5 counts these 5 partitions of 12: 1^2+1^2+..+1^2 = 1^2+1^2+...+1^2+2^2 = 1^2+1^2+..+1^2+2^2+2^2 = 1^2+1^2+1^2+3^2=2^2+2^2+2^2. Partitions with the divisors 4, 6 or 12 do not contribute to the count because 4^2, 6^2 and 12^2 are larger than n.

MAPLE

a := proc(n) coeftayl(1/mul(1-x^(d^2), d=numtheory[divisors](n)), x=0, n) ; end:

CROSSREFS

Cf. A018818, A001156, A002635.

Sequence in context: A238845 A093873 A305974 * A143773 A323524 A265893

Adjacent sequences:  A161145 A161146 A161147 * A161149 A161150 A161151

KEYWORD

nonn

AUTHOR

R. J. Mathar, Jun 03 2009

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 21 04:59 EDT 2019. Contains 321364 sequences. (Running on oeis4.)