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

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, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71

Offset: 1

Author

Reinhard Zumkeller, Jun 23 2003

Keywords

• nonn
• easy

Comments

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

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

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

Links

• Theodor Estermann, Einige Sätze über quadratfreie Zahlen, Mathematische Annalen 105:1 (1931), pp. 653-662.
• Eric Weisstein's World of Mathematics, Square Number
• Eric Weisstein's World of Mathematics, Squarefree

Programs

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