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A194545 Total sum of nonprime parts in all partitions of n. 5
0, 1, 2, 4, 11, 16, 33, 48, 89, 134, 214, 305, 478, 663, 976, 1356, 1934, 2617, 3654, 4877, 6652, 8808, 11772, 15386, 20329, 26308, 34249, 43987, 56651, 72079, 92008, 116171, 146967, 184381, 231399, 288398, 359581, 445426, 551721, 679868, 837238, 1026256 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = A066186(n) - A073118(n).

EXAMPLE

For n = 6 we have:

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

.                          Sum of

Partitions             nonprime parts

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

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

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

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

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

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

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

4 + 1 + 1 .................. 6

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

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

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

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

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

Total ..................... 33

So a(6) = 33.

MAPLE

b:= proc(n, i) option remember; local h, j, t;

      if n<0 then [0, 0]

    elif n=0 then [1, 0]

    elif i<1 then [0, 0]

    else h:= [0, 0];

         for j from 0 to iquo(n, i) do

           t:= b(n-i*j, i-1);

           h:= [h[1]+t[1], h[2]+t[2]+`if`(isprime(i), 0, t[1]*i*j)]

         od; h

      fi

    end:

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

seq(a(n), n=0..50);  # Alois P. Heinz, Nov 20 2011

MATHEMATICA

b[n_, i_] := b[n, i] = Module[{h, j, t}, Which[n<0, {0, 0}, n==0, {1, 0}, i < 1, {0, 0}, True, h = {0, 0}; For[j = 0, j <= Quotient[n, i], j++, t = b[n-i*j, i-1]; h = {h[[1]] + t[[1]], h[[2]] + t[[2]] + If[PrimeQ[i], 0, t[[1]]*i*j]}]; h]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 0, 50}] (* Jean-Fran├žois Alcover, Nov 03 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A018252, A066186, A073118, A194544.

Sequence in context: A023168 A134419 A024819 * A329800 A278346 A277867

Adjacent sequences:  A194542 A194543 A194544 * A194546 A194547 A194548

KEYWORD

nonn

AUTHOR

Omar E. Pol, Nov 20 2011

EXTENSIONS

More terms from Alois P. Heinz, Nov 20 2011

STATUS

approved

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)