login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A022544 Numbers that are not the sum of 2 squares. 47
3, 6, 7, 11, 12, 14, 15, 19, 21, 22, 23, 24, 27, 28, 30, 31, 33, 35, 38, 39, 42, 43, 44, 46, 47, 48, 51, 54, 55, 56, 57, 59, 60, 62, 63, 66, 67, 69, 70, 71, 75, 76, 77, 78, 79, 83, 84, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 102, 103, 105, 107, 108, 110, 111, 112, 114, 115, 118, 119, 120, 123, 124, 126, 127, 129, 131, 132, 133, 134, 135, 138, 139, 140, 141, 142, 143, 147, 150, 151, 152, 154, 155, 156, 158, 159, 161, 163, 165, 166, 167, 168, 171, 172, 174, 175, 176, 177, 179, 182, 183, 184, 186, 187, 188, 189, 190, 191, 192, 195, 198, 199 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: if n is not the sum of 2 squares sigma(n)==0 mod 4 (the converse does not hold, demonstrated by the entries in A025303). - Benoit Cloitre, May 19 2002

Numbers having some prime factor p == 3 (mod 4) to an odd power. sigma(n) == 0 (mod 4) because of this prime factor. Every n == 3 (mod 4) is an element. First differences are always 1, 2, 3 or 4, each occurring infinitely often. - David W. Wilson, Mar 09 2005

Complement of A000415 in the nonsquare positive integers A000037. - Max Alekseyev, Jan 21 2010

Integers with an equal number of 4k+1 and 4k+3 divisors. - Ant King, Oct 05 2010

A000161(a(n)) = 0; A070176(a(n)) > 0; A046712 is a subsequence. - Reinhard Zumkeller, Feb 04 2012, Aug 16 2011

There are arbitrarily long runs of consecutive terms. Record runs start at 3, 6, 21, 75, ... (A260157). - Ivan Neretin, Nov 09 2015

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 98-104.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

Steven R. Finch, Landau-Ramanujan Constant [Broken link]

Steven R. Finch, Landau-Ramanujan Constant [From the Wayback machine]

Index entries for sequences related to sums of squares

FORMULA

Lim_{n->inf} a(n)/n = 1.

MATHEMATICA

Select[Range[199], Length[PowersRepresentations[ #, 2, 2]] == 0 &] (* Ant King, Oct 05 2010 *)

Select[Range[200], SquaresR[2, #]==0&] (* Harvey P. Dale, Apr 21 2012 *)

PROG

(PARI) for(n=0, 200, if(sum(i=0, n, sum(j=0, i, if(i^2+j^2-n, 0, 1)))==0, print1((n), ", ")))

(PARI) is(n)=if(n%4==3, return(1)); my(f=factor(n)); for(i=1, #f~, if(f[i, 1]%4==3 && f[i, 2]%2, return(1))); 0 \\ Charles R Greathouse IV, Sep 01 2015

(Haskell)

import Data.List (elemIndices)

a022544 n = a022544_list !! (n-1)

a022544_list = elemIndices 0 a000161_list

-- Reinhard Zumkeller, Aug 16 2011

(MAGMA) [n: n in [0..160] | NormEquation(1, n) eq false]; // Vincenzo Librandi, Jan 15 2017

CROSSREFS

Complement of A001481; subsequence of A111909.

Cf. A018825, A025284, A000404, A007692.

Sequence in context: A101184 A087643 A248150 * A194366 A091067 A269177

Adjacent sequences:  A022541 A022542 A022543 * A022545 A022546 A022547

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Benoit Cloitre, May 19 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 19 02:29 EDT 2019. Contains 323377 sequences. (Running on oeis4.)