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!)
A326957 Total number of noncomposite parts in all partitions of n. 2
0, 1, 3, 6, 11, 19, 32, 50, 77, 115, 170, 244, 348, 486, 675, 923, 1253, 1682, 2246, 2968, 3904, 5094, 6616, 8533, 10962, 13997, 17808, 22538, 28426, 35689, 44670, 55678, 69199, 85692, 105826, 130261, 159935, 195778, 239092, 291191, 353854, 428925, 518848 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..42.

FORMULA

a(n) = A037032(n) + A000070(n-1), n >= 1.

a(n) = A006128(n) - A326981(n).

EXAMPLE

For n = 6 we have:

--------------------------------------

.                        Number of

Partitions             noncomposite

of 6                       parts

--------------------------------------

6 .......................... 0

3 + 3 ...................... 2

4 + 2 ...................... 1

2 + 2 + 2 .................. 3

5 + 1 ...................... 2

3 + 2 + 1 .................. 3

4 + 1 + 1 .................. 2

2 + 2 + 1 + 1 .............. 4

3 + 1 + 1 + 1 .............. 4

2 + 1 + 1 + 1 + 1 .......... 5

1 + 1 + 1 + 1 + 1 + 1 ...... 6

------------------------------------

Total ..................... 32

So a(6) = 32.

MAPLE

b:= proc(n, i) option remember; `if`(n=0 or i=1, [1, n], b(n, i-1)+

      (p-> p+[0, `if`(isprime(i), p[1], 0)])(b(n-i, min(n-i, i))))

    end:

a:= n-> b(n$2)[2]:

seq(a(n), n=0..50);  # Alois P. Heinz, Aug 13 2019

CROSSREFS

First differs from A183088 at a(13).

Cf. A000041, A000070, A006128, A008578 (noncomposites), A037032, A144115, A144116, A144119, A326958, A326981.

Sequence in context: A001976 A144115 A183088 * A116557 A001911 A020957

Adjacent sequences:  A326954 A326955 A326956 * A326958 A326959 A326960

KEYWORD

nonn

AUTHOR

Omar E. Pol, Aug 08 2019

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 27 15:39 EST 2020. Contains 332307 sequences. (Running on oeis4.)