A180161 Numbers that are the sum of two nonnegative squares but are not perfect powers.

2, 5, 10, 13, 17, 18, 20, 26, 29, 34, 37, 40, 41, 45, 50, 52, 53, 58, 61, 65, 68, 72, 73, 74, 80, 82, 85, 89, 90, 97, 98, 101, 104, 106, 109, 113, 116, 117, 122, 130, 136, 137, 145, 146, 148, 149, 153, 157, 160, 162, 164, 170, 173, 178, 180, 181, 185, 193, 194, 197, 200, 202, 205, 208, 212, 218, 221, 226, 229, 232, 233

Offset

1,1

Comments

Terms in A001481 but not in A001597.

Links

Table of n, a(n) for n=1..71.

Formula

Numbers of the form 2^i * S^j * T^(2*k) where S is a product of primes 4k+1, T a product of primes 4k+3, i,j,k>=0, and the gcd of the numbers {i, j, 2*k} is 1.

Prog

(PARI)
isA001481(n) =
{
    local(x=0, r=0);
    while(x<=sqrt(n)&r==0, if(issquare(n-x^2), r=1); x++);
    return(r);
}
for(n=2, 1000, if( isA001481(n) && !ispower(n), print1(n, ", ") ) );

Crossrefs

A001481 (sums of 2 nonnegative squares), A001597 (perfect powers).

Sequence in context: A046462 A188025 A187949 * A349243 A099261 A103215

Adjacent sequences: A180158 A180159 A180160 * A180162 A180163 A180164

Keyword

nonn

Author

Joerg Arndt, Jan 16 2011

Status

approved