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A326958 Total sum of noncomposite parts in all partitions of n. 2
0, 1, 4, 9, 16, 31, 52, 87, 132, 203, 303, 450, 641, 922, 1287, 1792, 2446, 3347, 4488, 6030, 7975, 10538, 13778, 17987, 23234, 29980, 38383, 49015, 62195, 78766, 99137, 124560, 155672, 194158, 241104, 298780, 368747, 454276, 557619, 683132, 834252, 1016955 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..41.

FORMULA

a(n) = A073118(n) + A000070(n-1), n >= 1.

a(n) = A066186(n) - A326982(n).

EXAMPLE

For n = 6 we have:

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

.                         Sum of

Partitions             noncomposite

of 6                       parts

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

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

3 + 3 ...................... 6

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

2 + 2 + 2 .................. 6

5 + 1 ...................... 6

3 + 2 + 1 .................. 6

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

2 + 2 + 1 + 1 .............. 6

3 + 1 + 1 + 1 .............. 6

2 + 1 + 1 + 1 + 1 .......... 6

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

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

Total ..................... 52

So a(6) = 52.

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]*i, 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

Cf. A000041, A000070, A008578 (noncomposites), A066186, A073118, A194545, A199936, A326957, A326982.

Sequence in context: A093175 A138992 A199936 * A281904 A007679 A239870

Adjacent sequences:  A326955 A326956 A326957 * A326959 A326960 A326961

KEYWORD

nonn

AUTHOR

Omar E. Pol, Aug 08 2019

STATUS

approved

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Last modified February 27 13:18 EST 2020. Contains 332306 sequences. (Running on oeis4.)