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A098235
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Number of ways to write n as a sum of two ordered positive squarefree numbers.
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3
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0, 1, 2, 3, 2, 3, 4, 6, 4, 3, 4, 7, 6, 5, 6, 10, 8, 8, 6, 11, 8, 9, 8, 14, 10, 9, 10, 13, 10, 9, 10, 16, 12, 13, 12, 22, 14, 13, 14, 22, 16, 15, 18, 25, 20, 15, 16, 26, 20, 16, 14, 27, 20, 20, 14, 26, 20, 21, 18, 29, 22, 21, 22, 30, 22, 21, 22, 35, 24, 25, 22, 42, 26, 27, 26, 39
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n) ~ n * Prod[p prime, (1-2/p^2) * Prod[p^2|n, (p^2-1)/(p^2-2)]].
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
P. Pollack, Analytic and Combinatorial Number Theory Course Notes, p. 122, 202. [?Broken link]
P. Pollack, Analytic and Combinatorial Number Theory Course Notes, p. 122, 202.
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FORMULA
| a(1)=0 then a(n+1)=sum(k=1,n,(mu(k)*mu(n+1-k))^2) - Benoit Cloitre (abmt(AT)orange.fr), Sep 24 2006
a(n+1) = SUM(A008966(k)*A008966(n-k+1): 1<=k<=n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 04 2009]
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EXAMPLE
| a(12)=7 because 12=1+11=2+10=5+7=6+6=7+5=10+2=11+1.
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CROSSREFS
| Cf. A005117, A098236.
Cf. A071068.
Sequence in context: A162751 A026342 A175266 * A114868 A138239 A112484
Adjacent sequences: A098232 A098233 A098234 * A098236 A098237 A098238
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KEYWORD
| nonn
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AUTHOR
| Ralf Stephan, Aug 31 2004
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