%I A002471 M0073 N0025
%S A002471 0,1,2,1,1,2,2,1,1,0,3,2,1,2,1,1,2,2,2,2,2,1,3,1,0,1,3,
%T A002471 2,2,2,1,3,2,0,2,1,1,4,2,1,3,2,2,2,2,1,4,2,1,1,2,2,3,3,
%U A002471 1,3,2,0,3,2,1,4,2,0,2,3,3,4,2,1,3,3,2,1,3,1,4,2,2,3,1
%N A002471 Number of partitions of n into a prime and a square.
%C A002471 a(A014090(n))=0; a(A014089(n))>0; a(A143989(n))=1. [From Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Sep 07 2008]
%D A002471 Selmer, Ernst S.; Eine numerische Untersuchung ueber die Darstellung 
               der natuerlichen Zahlen als Summe einer Primzahl und einer Quadratzahl. 
               Arch. Math. Naturvid. 47, (1943). no. 2, 21-39.
%D A002471 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002471 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002471 T. D. Noe, <a href="b002471.txt">Table of n, a(n) for n = 1..10000</a>
%p A002471 n->nops(select(isprime,[ seq(n-i^2,i=0..trunc(sqrt(n))) ])):
%p A002471 with(combstruct): specM0073 := {N=Prod(P, S),P=Set(Z,card>=1), S=Set(Z,
               card>=0)}: `combstruct/compile`(specM0073,unlabeled): `combstruct/
               Count`[ specM0073,unlabeled ][ P ] := proc(p) option remember; if 
               isprime(p) then 1 else 0 fi end: `combstruct/Count`[ specM0073,unlabeled 
               ][ S ] := proc(p) option remember; if type(sqrt(p), integer) then 
               1 else 0 fi end: M0073 := n->count([ N,specM0073,unlabeled ],size=n):
%Y A002471 A064272. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Sep 07 2008]
%Y A002471 Sequence in context: A034798 A115236 A064286 this_sequence A091243 A037826 
               A079882
%Y A002471 Adjacent sequences: A002468 A002469 A002470 this_sequence A002472 A002473 
               A002474
%K A002471 nonn,nice
%O A002471 1,3
%A A002471 N. J. A. Sloane (njas(AT)research.att.com).
%E A002471 Sequence corrected by Paul Zimmermann Mar 15 1996