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A326958 Total sum of noncomposite parts in all partitions of n. 2

%I

%S 0,1,4,9,16,31,52,87,132,203,303,450,641,922,1287,1792,2446,3347,4488,

%T 6030,7975,10538,13778,17987,23234,29980,38383,49015,62195,78766,

%U 99137,124560,155672,194158,241104,298780,368747,454276,557619,683132,834252,1016955

%N Total sum of noncomposite parts in all partitions of n.

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

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

%e For n = 6 we have:

%e --------------------------------------

%e . Sum of

%e Partitions noncomposite

%e of 6 parts

%e --------------------------------------

%e 6 .......................... 0

%e 3 + 3 ...................... 6

%e 4 + 2 ...................... 2

%e 2 + 2 + 2 .................. 6

%e 5 + 1 ...................... 6

%e 3 + 2 + 1 .................. 6

%e 4 + 1 + 1 .................. 2

%e 2 + 2 + 1 + 1 .............. 6

%e 3 + 1 + 1 + 1 .............. 6

%e 2 + 1 + 1 + 1 + 1 .......... 6

%e 1 + 1 + 1 + 1 + 1 + 1 ...... 6

%e ------------------------------------

%e Total ..................... 52

%e So a(6) = 52.

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

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

%p end:

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

%p seq(a(n), n=0..50); # _Alois P. Heinz_, Aug 13 2019

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

%K nonn

%O 0,3

%A _Omar E. Pol_, Aug 08 2019

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Last modified March 28 05:38 EDT 2020. Contains 333073 sequences. (Running on oeis4.)