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A085265 Numbers that can be written as sum of a positive squarefree number and a positive square. 5

%I

%S 2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,

%T 28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,

%U 51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71

%N Numbers that can be written as sum of a positive squarefree number and a positive square.

%C Subsequence of A011760; A085263(a(n)) > 0.

%C Conjecture: a(n) = n + 2 for n > 11. That is, only 1 and 13 are missing. - _Charles R Greathouse IV_, Aug 21 2011

%C Estermann proves that only finitely many positive integers are missing from this sequence. (Probably only 1 and 13.) - _Charles R Greathouse IV_, Jul 01 2016

%H Theodor Estermann, <a href="https://eudml.org/doc/159528">Einige Sätze über quadratfreie Zahlen</a>, Mathematische Annalen 105:1 (1931), pp. 653-662.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SquareNumber.html">Square Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>

%o (PARI) is(n)=forstep(k=sqrtint(n-1), 1, -1, if(issquarefree(n-k^2), return(1))); 0 \\ _Charles R Greathouse IV_, Mar 12, 2012

%K nonn,easy

%O 1,1

%A _Reinhard Zumkeller_, Jun 23 2003

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Last modified December 11 03:18 EST 2016. Contains 279034 sequences.