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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 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 MATHEMATICA b[n_, i_] := b[n, i] = If[n==0 || i==1, {1, 0}, b[n, i-1] + # + {0, If[PrimeQ[i], 0, #[[1]]]}&[b[n-i, Min[n-i, i]]]]; a[n_] := b[n, n][[2]]; a /@ Range[0, 50] (* Jean-François Alcover, Nov 17 2020, after Alois P. Heinz *) CROSSREFS Cf. A000041, A002808, A006128, A037032, A144115, A144116, A144119, A326957, A326982. Sequence in context: A339996 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 June 15 13:33 EDT 2021. Contains 345048 sequences. (Running on oeis4.)