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A326981 Total number of composite parts in all partitions of n. 2
0, 0, 0, 0, 1, 1, 3, 4, 9, 13, 22, 31, 51, 70, 105, 145, 210, 283, 398, 530, 726, 958, 1283, 1673, 2212, 2854, 3714, 4756, 6119, 7764, 9893, 12457, 15728, 19674, 24636, 30615, 38079, 47034, 58109, 71396, 87692, 107179, 130943, 159278, 193619, 234486, 283720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..46.

FORMULA

a(n) = A144119(n) - A000070(n-1), n >= 1.

a(n) = A006128(n) - A326957(n).

EXAMPLE

For n = 6 we have:

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

.                        Number of

Partitions               composite

of 6                       parts

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

6 .......................... 1

3 + 3 ...................... 0

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

2 + 2 + 2 .................. 0

5 + 1 ...................... 0

3 + 2 + 1 .................. 0

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

2 + 2 + 1 + 1 .............. 0

3 + 1 + 1 + 1 .............. 0

2 + 1 + 1 + 1 + 1 .......... 0

1 + 1 + 1 + 1 + 1 + 1 ...... 0

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

Total ...................... 3

So a(6) = 3.

MAPLE

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

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

Cf. A000041, A002808, A006128, A037032, A144115, A144116, A144119, A326957, A326982.

Sequence in context: A116552 A225288 A167930 * A124285 A131326 A089300

Adjacent sequences:  A326978 A326979 A326980 * A326982 A326983 A326984

KEYWORD

nonn

AUTHOR

Omar E. Pol, Aug 09 2019

STATUS

approved

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Last modified September 25 22:02 EDT 2020. Contains 337344 sequences. (Running on oeis4.)