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A326982 Total sum of composite parts in all partitions of n. 3
0, 0, 0, 0, 4, 4, 14, 18, 44, 67, 117, 166, 283, 391, 603, 848, 1250, 1702, 2442, 3280, 4565, 6094, 8266, 10878, 14566, 18970, 24953, 32255, 41909, 53619, 68983, 87542, 111496, 140561, 177436, 222125, 278425, 346293, 430951, 533083, 659268, 810948, 997322 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..8000

FORMULA

a(n) = A194545(n) - A000070(n-1), n >= 1.

a(n) = A066186(n) - A326958(n).

EXAMPLE

For n = 6 we have:

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

Partitions                Sum of

of 6                  composite parts

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

6 .......................... 6

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

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

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

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

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

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

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

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

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

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

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

Total ..................... 14

So a(6) = 14.

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]*i)])(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, A066186, A073118, A194544, A194545, A199936, A326958, A326981.

Sequence in context: A263870 A263796 A263871 * A263797 A331609 A174406

Adjacent sequences:  A326979 A326980 A326981 * A326983 A326984 A326985

KEYWORD

nonn

AUTHOR

Omar E. Pol, Aug 09 2019

STATUS

approved

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Last modified April 7 15:56 EDT 2020. Contains 333306 sequences. (Running on oeis4.)