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A064272 Number of representations of n as the sum of a prime number and a nonzero square. 8
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 14 17:09 EST 2018. Contains 318103 sequences. (Running on oeis4.)