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 A064272 Number of representations of n as the sum of a prime number and a nonzero square. 9
 0, 1, 1, 0, 2, 1, 1, 1, 0, 2, 2, 0, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 0, 1, 3, 2, 1, 2, 0, 3, 2, 0, 2, 1, 0, 4, 2, 1, 2, 2, 1, 2, 2, 1, 3, 2, 1, 1, 2, 2, 2, 3, 1, 3, 2, 0, 2, 2, 0, 4, 2, 0, 2, 3, 2, 4, 2, 1, 2, 3, 1, 1, 3, 1, 4, 2, 1, 3, 1, 1, 5, 3, 0, 3, 3, 2, 2, 2, 0, 4, 2, 1, 3, 2, 1, 4, 1, 1, 2, 3, 2, 3, 4, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,5 COMMENTS a(A064233(n))=0. A002471(n) - 1 <= a(n) <= A002471(n). [Reinhard Zumkeller, Sep 30 2011] A224076(n) <= a(A214583(n)+1) for n such that A214583 is defined; a(A064283(n)) = n and a(m) <> n for m < A064283(n). - Reinhard Zumkeller, Mar 31 2013 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 2..10000 FORMULA a(n) = SUM(A010051(k)*A010052(n-k+1): 1<=k<=n). [From Reinhard Zumkeller, Nov 05 2009] G.f.: (Sum_{k>=1} x^prime(k))*(Sum_{k>=1} x^(k^2)). - Ilya Gutkovskiy, Feb 05 2017 EXAMPLE 6=2+4=5+1, thus a(6)=2. PROG (Haskell) a064272 n = sum \$ map (a010051 . (n -)) \$ takeWhile (< n) \$ tail a000290_list -- Reinhard Zumkeller, Jul 23 2013, Sep 30 2011 CROSSREFS Cf. A064233. Cf. A000290. Sequence in context: A135936 A109707 A214578 * A117479 A200650 A281743 Adjacent sequences: A064269 A064270 A064271 * A064273 A064274 A064275 KEYWORD nonn AUTHOR Vladeta Jovovic, Sep 23 2001 STATUS approved

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Last modified December 8 13:24 EST 2023. Contains 367679 sequences. (Running on oeis4.)