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A050804 Numbers n such that n^3 is the sum of two nonzero squares in exactly one way. 4
2, 8, 18, 32, 72, 98, 128, 162, 242, 288, 392, 512, 648, 722, 882, 968, 1058, 1152, 1458, 1568, 1922, 2048, 2178, 2592, 2888, 3528, 3698, 3872, 4232, 4418, 4608, 4802, 5832, 6272, 6498, 6962, 7688, 7938, 8192 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

m is a term if and only if m = 2^(2a_0+1)*p_1^(2a_1)*p_2^(2a_2)*...*p_k^(2a_k), where a_i are nonnegative integers and p_i are primes of the form 4k+3. - Chai Wah Wu, Feb 27 2016

m is a term if and only if for all odd q > 1, m^q is the sum of two nonzero squares in exactly one way. - Chai Wah Wu, Feb 28 2016

Numbers n such that n is the sum of two nonzero squares while n^2 is not. - Altug Alkan, Apr 11 2016

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sums of squares

FORMULA

n such that A084888(n) = 1.

EXAMPLE

E.g. 32^3 = 128^2 + 128^2. Is there an example using different squares?

No: If n^3 has only one representation as n^3 = a^2+b^2 with 0<a<=b, then a=b. - Jonathan Vos Post, Feb 02 2011

MATHEMATICA

ok[n_] := Length @ Cases[ PowersRepresentations[n^3, 2, 2], {_?Positive, _?Positive}] == 1; Select[Range[8200], ok] (* Jean-Fran├žois Alcover, Apr 05 2011 *)

PROG

(Haskell)

a050804 n = a050804_list !! (n-1)

a050804_list = filter ((== 1) . a084888) [0..]

-- Reinhard Zumkeller, Jul 18 2012

(Python)

from sympy import factorint

A050804_list = [2*i for i in range(1, 10**6) if not any(p % 4 == 1 or factorint(i)[p] % 2 for p in factorint(i))] # Chai Wah Wu, Feb 27 2016

CROSSREFS

Cf. A000404, A050803.

Cf. A081324.

Sequence in context: A001105 A336489 A051787 * A081324 A190787 A018229

Adjacent sequences:  A050801 A050802 A050803 * A050805 A050806 A050807

KEYWORD

nonn,nice

AUTHOR

Patrick De Geest, Sep 15 1999

EXTENSIONS

More terms from Michel ten Voorde and Jud McCranie

STATUS

approved

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Last modified September 19 06:21 EDT 2021. Contains 347551 sequences. (Running on oeis4.)