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

1,1

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

Table of n, a(n) for n=1..69.

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

Prog

(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

Crossrefs

Sequence in context: A191431 A191430 A011760 * A180004 A252474 A172270

Adjacent sequences: A085262 A085263 A085264 * A085266 A085267 A085268

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jun 23 2003

Status

approved