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A274595 Numbers n such that n^2 + 2 is the sum of two nonzero squares. 2
0, 4, 12, 24, 40, 48, 60, 68, 72, 84, 104, 112, 132, 140, 144, 148, 176, 180, 192, 204, 216, 220, 252, 264, 276, 284, 312, 320, 324, 364, 372, 384, 392, 396, 408, 420, 428, 444, 456, 468, 472, 480, 528, 544, 588, 600, 612, 624, 636, 644, 648, 660, 684, 688, 708, 720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

All terms are divisible by 4.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

12 is a term because 12^2 + 2 = 5^2 + 11^2.

MAPLE

f:= n -> andmap(t -> t[1] mod 4 <> 3 or t[2]::even, ifactors(n^2+2)[2]):

map(f, [seq(n, n=4..1000, 4)]); # Robert Israel, Jul 12 2016

MATHEMATICA

stnsQ[n_]:=Length[Select[IntegerPartitions[n^2+2, {2}], AllTrue[Sqrt[ #], IntegerQ]&]]>0; Select[Range[0, 750, 4], stnsQ]  (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 11 2020 *)

PROG

(PARI) isA000404(n) = for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2));

lista(nn) = for(n=0, nn, if(isA000404(n^2+2), print1(n, ", ")));

CROSSREFS

Cf. A000404, A059100.

Sequence in context: A301058 A008213 A008187 * A115228 A081935 A008006

Adjacent sequences:  A274592 A274593 A274594 * A274596 A274597 A274598

KEYWORD

nonn,easy

AUTHOR

Altug Alkan, Jun 30 2016

STATUS

approved

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Last modified September 18 01:39 EDT 2021. Contains 347504 sequences. (Running on oeis4.)