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

2,5

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