A062602 - OEIS

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A062602

Number of ways of writing n = p+c with p prime and c nonprime (1 or a composite number).

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; internal format)

	OFFSET	`1,6`
	LINKS	`Index entries for sequences related to Goldbach conjecture` `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 (reinhard.zumkeller(AT)gmail.com), Nov 05 2009]`
	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.`
	CROSSREFS	`Cf. A061358, A014092, A062610.` `Sequence in context: A035436 A035369 A129719 * A123148 A173410 A166548` `Adjacent sequences: A062599 A062600 A062601 * A062603 A062604 A062605`
	KEYWORD	`nonn`
	AUTHOR	`Labos E. (labos(AT)ana.sote.hu), Jul 04 2001`

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Last modified February 17 20:50 EST 2012. Contains 206085 sequences.