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!)
A340693 Number of integer partitions of n where each part is a divisor of the number of parts. 7
1, 1, 1, 2, 2, 3, 2, 5, 5, 7, 7, 10, 10, 14, 14, 17, 19, 24, 24, 32, 33, 42, 43, 58, 59, 75, 79, 98, 104, 124, 128, 156, 166, 196, 204, 239, 251, 292, 306, 352, 372, 426, 445, 514, 543, 616, 652, 745, 790, 896, 960, 1080, 1162, 1311, 1400, 1574, 1692, 1892 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The only strict partitions counted are (), (1), and (2,1).

Is there a simple generating function?

LINKS

Table of n, a(n) for n=0..57.

EXAMPLE

The a(1) = 1 through a(9) = 7 partitions:

  1  11  21   22    311    2211    331      2222      333

         111  1111  2111   111111  2221     4211      4221

                    11111          4111     221111    51111

                                   211111   311111    222111

                                   1111111  11111111  321111

                                                      21111111

                                                      111111111

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], And@@IntegerQ/@(Length[#]/#)&]], {n, 0, 30}]

CROSSREFS

Note: Heinz numbers are given in parentheses below.

The reciprocal version is A143773 (A316428), with strict case A340830.

The case where length also divides n is A326842 (A326847).

The Heinz numbers of these partitions are A340606.

The version for factorizations is A340851, with reciprocal version A340853.

A018818 counts partitions of n into divisors of n (A326841).

A047993 counts balanced partitions (A106529).

A067538 counts partitions of n whose length/max divides n (A316413/A326836).

A067539 counts partitions with integer geometric mean (A326623).

A072233 counts partitions by sum and length.

A168659 = partitions whose greatest part divides their length (A340609).

A168659 = partitions whose length divides their greatest part (A340610).

A326843 = partitions of n whose length and maximum both divide n (A326837).

A330950 = partitions of n whose Heinz number is divisible by n (A324851).

Cf. A000041, A003114, A006141, A033630, A064174, A074761, A102627, A200750, A237984, A298423, A340827.

Sequence in context: A050323 A318286 A214646 * A275382 A199583 A157922

Adjacent sequences:  A340690 A340691 A340692 * A340694 A340695 A340696

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 23 2021

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 January 17 04:46 EST 2022. Contains 350378 sequences. (Running on oeis4.)