A064272 Number of representations of n as the sum of a prime number and a nonzero square.

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

Offset: 2

Author

Vladeta Jovovic, Sep 23 2001

Keywords

• nonn

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

Examples

			6=2+4=5+1, thus a(6)=2.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A064233.

Cf. A000290.

Programs

Haskell

a064272 n = sum $
   map (a010051 . (n -)) $ takeWhile (< n) $ tail a000290_list
-- Reinhard Zumkeller, Jul 23 2013, Sep 30 2011

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