A268183 Values of a^2 + b^2 such that sigma(a^2 + b^2) is of the form x^2 + y^2 where a, b, x, y are nonzero integers.

10, 17, 40, 52, 58, 73, 89, 90, 97, 106, 145, 153, 193, 202, 232, 233, 241, 250, 298, 313, 337, 338, 346, 360, 409, 416, 424, 449, 457, 468, 505, 521, 522, 538, 577, 586, 634, 640, 657, 673, 680, 724, 730, 745, 778, 801, 808, 809, 810, 845, 865, 873, 881, 890, 953, 954, 976, 986, 1000

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

10 is a term because 10 = 1^2 + 3^2 and 10 is divisible by 1, 2, 5, 10 and 1 + 2 + 5 + 10 = 3^2 + 3^2.

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=1, nn, if(isA000404(n) && isA000404(sigma(n)), print1(n, ", ")));
(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))
list(lim)=my(v=List(), x2, t); lim\=1; for(x=1, sqrtint(lim-1), x2=x^2; for(y=1, sqrtint(lim-x2), if(isA000404(sigma(t=x2+y^2)), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Apr 30 2016

Crossrefs

Cf. A000203, A000404.

Sequence in context: A364823 A019991 A164285 * A293690 A069546 A065018

Adjacent sequences: A268180 A268181 A268182 * A268184 A268185 A268186

Keyword

nonn

Author

Altug Alkan, Apr 30 2016

Status

approved