cp's OEIS Frontend

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

%I A064272 #18 Feb 05 2017 13:16:17
%S A064272 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,
%T A064272 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,
%U A064272 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
%N A064272 Number of representations of n as the sum of a prime number and a nonzero square.
%C A064272 a(A064233(n))=0.
%C A064272 A002471(n) - 1 <= a(n) <= A002471(n). [_Reinhard Zumkeller_, Sep 30 2011]
%C A064272 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
%H A064272 Reinhard Zumkeller, <a href="/A064272/b064272.txt">Table of n, a(n) for n = 2..10000</a>
%F A064272 a(n) = SUM(A010051(k)*A010052(n-k+1): 1<=k<=n). [From _Reinhard Zumkeller_, Nov 05 2009]
%F A064272 G.f.: (Sum_{k>=1} x^prime(k))*(Sum_{k>=1} x^(k^2)). - _Ilya Gutkovskiy_, Feb 05 2017
%e A064272 6=2+4=5+1, thus a(6)=2.
%o A064272 (Haskell)
%o A064272 a064272 n = sum $
%o A064272    map (a010051 . (n -)) $ takeWhile (< n) $ tail a000290_list
%o A064272 -- _Reinhard Zumkeller_, Jul 23 2013, Sep 30 2011
%Y A064272 Cf. A064233.
%Y A064272 Cf. A000290.
%K A064272 nonn
%O A064272 2,5
%A A064272 _Vladeta Jovovic_, Sep 23 2001