A302771 If there is Gaussian integer z such that the norm of z is n, a(n) is the absolute value of Product_{the norm of z is n} z. Otherwise a(n) = 0.

0, 1, 4, 0, 16, 625, 0, 0, 64, 81, 10000, 0, 0, 28561, 0, 0, 256, 83521, 324, 0, 160000, 0, 0, 0, 0, 244140625, 456976, 0, 0, 707281, 0, 0, 1024, 0, 1336336, 0, 1296, 1874161, 0, 0, 2560000, 2825761, 0, 0, 0, 4100625, 0, 0, 0, 2401, 15625000000, 0, 7311616, 7890481, 0, 0

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

If A004018(n) > 0, a(n) = n^(A004018(n)/2). Otherwise a(n) = 0.

Example

The Gaussian integers whose norm is 5;
    *   *      -1+2i, 1+2i
  *       *    -2+i,  2+i
-------------
  *       *    -2-i,  2-i
    *   *      -1-2i, 1-2i
               a(5) = (2+i)*(2-i)*(1+2i)*(1-2i)*(-1+2i)*(-1-2i)*(-2+i)*(-2-i) = 625.

Crossrefs

Cf. A004018.

Sequence in context: A343473 A375992 A233807 * A378618 A167350 A215669

Adjacent sequences: A302768 A302769 A302770 * A302772 A302773 A302774

Keyword

nonn

Author

Seiichi Manyama, Apr 13 2018

Status

approved