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 A326957 Total number of noncomposite parts in all partitions of n. 2
 0, 1, 3, 6, 11, 19, 32, 50, 77, 115, 170, 244, 348, 486, 675, 923, 1253, 1682, 2246, 2968, 3904, 5094, 6616, 8533, 10962, 13997, 17808, 22538, 28426, 35689, 44670, 55678, 69199, 85692, 105826, 130261, 159935, 195778, 239092, 291191, 353854, 428925, 518848 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n) = A037032(n) + A000070(n-1), n >= 1. a(n) = A006128(n) - A326981(n). EXAMPLE For n = 6 we have: -------------------------------------- .                        Number of Partitions             noncomposite of 6                       parts -------------------------------------- 6 .......................... 0 3 + 3 ...................... 2 4 + 2 ...................... 1 2 + 2 + 2 .................. 3 5 + 1 ...................... 2 3 + 2 + 1 .................. 3 4 + 1 + 1 .................. 2 2 + 2 + 1 + 1 .............. 4 3 + 1 + 1 + 1 .............. 4 2 + 1 + 1 + 1 + 1 .......... 5 1 + 1 + 1 + 1 + 1 + 1 ...... 6 ------------------------------------ Total ..................... 32 So a(6) = 32. 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], 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 First differs from A183088 at a(13). Cf. A000041, A000070, A006128, A008578 (noncomposites), A037032, A144115, A144116, A144119, A326958, A326981. Sequence in context: A001976 A144115 A183088 * A116557 A001911 A020957 Adjacent sequences:  A326954 A326955 A326956 * A326958 A326959 A326960 KEYWORD nonn AUTHOR Omar E. Pol, Aug 08 2019 STATUS approved

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Last modified February 27 15:39 EST 2020. Contains 332307 sequences. (Running on oeis4.)