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!)
A305736 Number of integer partitions of n whose greatest common divisor is composite (nonprime and > 1). 0
0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 4, 0, 1, 1, 5, 0, 4, 0, 8, 1, 1, 0, 14, 1, 1, 3, 16, 0, 10, 0, 22, 1, 1, 1, 41, 0, 1, 1, 45, 0, 18, 0, 57, 9, 1, 0, 94, 1, 8, 1, 102, 0, 38, 1, 138, 1, 1, 0, 221, 0, 1, 17, 231, 1, 59, 0, 298, 1, 22 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

Table of n, a(n) for n=1..70.

FORMULA

a(n) = A018783(n) - A305735(n) for n > 0. - Andrew Howroyd, Jun 22 2018

EXAMPLE

The a(12) = 4 integer partitions are (12), (8 4), (6 6), (4 4 4).

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], !(GCD@@#==1||PrimeQ[GCD@@#])&]], {n, 0, 20}]

PROG

(PARI) seq(n)={concat([1], dirmul(vector(n, n, numbpart(n)), dirmul(vector(n, n, moebius(n)), vector(n, n, n>1&&!isprime(n)))))} \\ Andrew Howroyd, Jun 22 2018

CROSSREFS

Cf. A000040, A000837, A018783, A100953, A289508, A302698, A305563, A305731, A305735.

Sequence in context: A318758 A124790 A325734 * A324642 A326757 A147787

Adjacent sequences:  A305733 A305734 A305735 * A305737 A305738 A305739

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 22 2018

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 February 25 11:39 EST 2020. Contains 332233 sequences. (Running on oeis4.)