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A008784
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Numbers n such that sqrt(-1) mod n exists; or, numbers n that are primitively represented by x^2+y^2.
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29
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1, 2, 5, 10, 13, 17, 25, 26, 29, 34, 37, 41, 50, 53, 58, 61, 65, 73, 74, 82, 85, 89, 97, 101, 106, 109, 113, 122, 125, 130, 137, 145, 146, 149, 157, 169, 170, 173, 178, 181, 185, 193, 194, 197, 202, 205, 218, 221, 226, 229, 233, 241, 250, 257, 265, 269, 274, 277, 281, 289
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Numbers whose prime divisors all congruent to 1 mod 4, with the exception of at most a single factor of 2. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 07 2008]
In appears that a(n) is the set of proper divisors of numbers of the type n^2+1 [From Kaloyan Todorov (kaloyan.todorov(AT)gmail.com), Mar 25 2009]. This conjecture is correct. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 07 2009
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REFERENCES
| B. C. Berndt & R. A. Rankin, Ramanujan: Letters and Commentary, see p. 176; AMS Providence RI 1995.
Dickson, Leonard Eugene; History of the Theory Of Numbers, Volume II: Diophantine Analysis, Chelsea Publishing Company, 1992, pp.230-242. [From Ant King (mathstutoring(AT)ntlworld.com), Oct 11 2010]
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| If a(n) is a member of this sequence, then so too are all of its divisors (Euler). [From Ant King (mathstutoring(AT)ntlworld.com), Oct 11 2010]
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MAPLE
| with(numtheory); [seq(mroot(-1, 2, p), p=1..300)];
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MATHEMATICA
| data=Flatten[FindInstance[x^2+y^2==# && 0<=x<=# && 0<=y<=# && GCD[x, y]==1, {x, y}, Integers]&/@Range[289], 1]; x^2+y^2/.data//DeleteDuplicates [From Ant King (mathstutoring(AT)ntlworld.com), Oct 11 2010]
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CROSSREFS
| Cf. A001481, A022544, A020893, A037942, A034023-, A057756.
Indices of nonzero entries in A076948. This follows from G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Ch. 20.2-3. - Amarnath Murthy and Vladeta Jovovic, Oct 20, 2002
Cf. A045673.
Sequence in context: A099261 A103215 A037942 * A020893 A145017 A003814
Adjacent sequences: A008781 A008782 A008783 * A008785 A008786 A008787
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
| Checked by T. D. Noe, Apr 19 2007
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