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A004613
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Numbers that are divisible only by primes congruent to 1 mod 4.
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14
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1, 5, 13, 17, 25, 29, 37, 41, 53, 61, 65, 73, 85, 89, 97, 101, 109, 113, 125, 137, 145, 149, 157, 169, 173, 181, 185, 193, 197, 205, 221, 229, 233, 241, 257, 265, 269, 277, 281, 289, 293, 305, 313, 317, 325, 337, 349, 353, 365, 373, 377, 389, 397, 401, 409, 421
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also gives solutions z to x^2+y^2=z^4 with GCD(x,y,z)=1 and x,y,z positive. - John Sillcox (johnsillcox(AT)hotmail.com), Feb 20 2004
A065338(a(n)) = 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 10 2010]
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REFERENCES
| D. Cox, "Primes of Form x^2 + n y^2", Wiley, 1989.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
| Numbers of the form x^2+y^2 where x is even, y is odd and gcd(x, y) = 1.
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MATHEMATICA
| ok[1] = True; ok[n_] := And @@ (Mod[#, 4] == 1 &) /@ FactorInteger[n][[All, 1]]; Select[Range[421], ok] (* From Jean-François Alcover, May 05 2011 *)
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PROG
| (PARI) for(n=1, 1000, if(sumdiv(n, d, isprime(d)*if((d-1)%4, 1, 0))==0, print1(n, ", ")))
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CROSSREFS
| Essentially same as A008846.
Cf. A004614.
Sequence in context: A087445 A020882 A081804 * A008846 A162597 A120960
Adjacent sequences: A004610 A004611 A004612 * A004614 A004615 A004616
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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