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 A062602 Number of ways of writing n = p+c with p prime and c nonprime (1 or a composite number). 14
 0, 0, 1, 1, 0, 2, 1, 2, 2, 1, 4, 3, 3, 3, 4, 2, 6, 3, 5, 4, 6, 3, 8, 3, 7, 4, 9, 5, 9, 4, 8, 7, 9, 4, 11, 3, 11, 9, 10, 6, 12, 5, 11, 8, 12, 7, 14, 5, 13, 7, 15, 9, 15, 6, 14, 10, 16, 9, 16, 5, 15, 13, 16, 8, 18, 6, 18, 15, 17, 9, 19, 8, 18, 12, 19, 11, 21, 7, 21, 14, 20, 13, 22, 7, 21, 14 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 LINKS Donovan Johnson, Table of n, a(n) for n = 1..10000 FORMULA a(n+1) = SUM(A010051(k)*A005171(n-k+1): 1<=k<=n). [From Reinhard Zumkeller, Nov 05 2009] a(n) + A061358(n) + A062610(n) = A004526(n). - R. J. Mathar, Sep 10 2021 EXAMPLE n = 22 has floor(n/2) = 11 partitions of form n = a + b; 3 partitions are of prime + prime [3 + 19 = 5 + 17 = 11 + 11], 3 partitions are of prime + nonprime [2 + 20 = 7 + 15 = 13 + 9], 5 partitions are nonprime + nonprime [1 + 21 = 4 + 18 = 6 + 16 = 8 + 14 = 10 + 12]. So a(22) = 3. MATHEMATICA Table[Length[Select[Range[Floor[n/2]], (PrimeQ[#] && Not[PrimeQ[n - #]]) || (Not[PrimeQ[#]] && PrimeQ[n - #]) &]], {n, 80}] (* Alonso del Arte, Apr 21 2013 *) Table[Length[Select[IntegerPartitions[n, {2}], AnyTrue[#, PrimeQ] && !AllTrue[ #, PrimeQ]&]], {n, 90}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 19 2020 *) CROSSREFS Cf. A061358, A014092, A062610, A224712. Sequence in context: A242210 A035369 A129719 * A123148 A173410 A166548 Adjacent sequences:  A062599 A062600 A062601 * A062603 A062604 A062605 KEYWORD nonn,easy AUTHOR Labos Elemer, Jul 04 2001 STATUS approved

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Last modified September 25 09:35 EDT 2022. Contains 356977 sequences. (Running on oeis4.)