A216679 Numbers which can be written neither as a^2+b^2, nor as a^2+2*b^2, nor as a^2+3*b^2, nor as a^2+7*b^2, with a >= 0 and b >= 0.

14, 15, 30, 35, 42, 46, 47, 55, 60, 62, 69, 70, 78, 87, 94, 95, 105, 110, 115, 119, 120, 126, 135, 138, 140, 141, 142, 143, 154, 155, 158, 159, 165, 167, 168, 174, 182, 186, 188, 190, 195, 206, 210, 213, 215, 220, 222, 230, 231, 235, 238, 240, 248, 254, 255, 266, 270, 276, 280, 282, 285, 286, 287, 295, 299

Offset

1,1

Comments

If a composite number C, in case, can be written in the form C = a^2+k*b^2, for some integers a & b, then every prime factor P (for C) being raised to an odd power can be written in the form P = c^2+k*d^2, for some integers c & d.

This statement is only true for k = 1, 2, 3.

For k = 7, with the exception of the prime factor 2, the statement mentioned above is true.

Links

Table of n, a(n) for n=1..65.

Crossrefs

Cf. A216451, A216500.

Sequence in context: A041392 A042631 A344977 * A216680 A332736 A162283

Adjacent sequences: A216676 A216677 A216678 * A216680 A216681 A216682

Keyword

nonn

Author

V. Raman, Sep 13 2012

Status

approved