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A264732 Löschian numbers (A003136) which are the sum of 2 nonzero squares. 1
13, 25, 37, 52, 61, 73, 97, 100, 109, 117, 148, 157, 169, 181, 193, 208, 225, 229, 241, 244, 277, 289, 292, 313, 325, 333, 337, 349, 373, 388, 397, 400, 409, 421, 433, 436, 457, 468, 481, 541, 549, 577, 592, 601, 613, 625, 628, 637, 657, 661, 673, 676, 709, 724, 733 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

n is in the sequence iff 4*n is.

If a(n) is a prime number, a(n) mod 12 = 1.

Prime terms of sequence are listed in A068228 that lists generalized cuban primes (A007645) which are the sum of 2 nonzero squares.

Also positive numbers of the form x^2 - 3*y^2 (A084916) that are the sum of 2 nonzero squares. - Frank M Jackson, Oct 13 2019

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

a(1) = 13 because 13 = 3^2 + 3*1 + 1^2 = 3^2 + 2^2.

a(2) = 25 because 25 = 5^2 + 5*0 + 0^2 = 4^2 + 3^2.

a(3) = 37 because 37 = 4^2 + 4*3 + 3^2 = 6^2 + 1^2.

MATHEMATICA

Select[Range@750, Length[PowersRepresentations[#, 2, 2] /. {0, _}->Nothing]>0 && Reduce[#==x^2+x*y+y^2, {x, y}, Integers]=!=False &] (* Frank M Jackson, Oct 13 2019 *)

PROG

(PARI) isok(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))}

is(n) = #bnfisintnorm(bnfinit(z^2+z+1), n);

for(n=1, 1e3, if( is(n) && isok(n), print1(n, ", ")))

CROSSREFS

Cf. A000404, A003136, A068228, A084916.

Sequence in context: A075033 A017533 A309809 * A298483 A195558 A026058

Adjacent sequences:  A264729 A264730 A264731 * A264733 A264734 A264735

KEYWORD

nonn

AUTHOR

Altug Alkan, Nov 22 2015

STATUS

approved

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Last modified March 30 22:55 EDT 2020. Contains 333132 sequences. (Running on oeis4.)