A121051 Semiprimes which are sums of 4 but no fewer nonzero squares.

15, 39, 55, 87, 95, 111, 119, 143, 159, 183, 215, 247, 287, 295, 303, 319, 327, 335, 391, 407, 415, 447, 471, 511, 519, 527, 535, 543, 551, 559, 583, 591, 623, 655, 671, 679, 687, 695, 703, 767, 791, 799, 807, 815, 831, 871, 879, 895, 943, 951, 959, 1007

Offset: 1

Author

Jonathan Vos Post, Aug 08 2006

Keywords

• easy
• nonn
• less

Comments

Semiprime analog of A007522 Primes of form 8n+7. These semiprimes must all be numbers of the form 4^i(8j+7), i >= 0, j >= 0. However, for positive i, 4^i(8j+7) has more than 2 prime factors (with multiplicity). Hence from Legendre's corollary to Lagrange's Four-Square Theorem, this sequence is precisely Semiprimes of the form 8*k+7.

Crossrefs

A001358 intersect A004215.

Cf. A001358, A004215, A007522.

Programs

Mathematica

Select[8*Range[200]+7,PrimeOmega[#]==2&] (* Harvey P. Dale, Oct 28 2017 *)

Extensions

a(15)-a(52) from Giovanni Resta, Jun 13 2016