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

1,1

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.

Links

Table of n, a(n) for n=1..52.

Mathematica

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

Crossrefs

A001358 intersect A004215.

Cf. A001358, A004215, A007522.

Sequence in context: A336560 A176257 A055131 * A139042 A020142 A146696

Adjacent sequences: A121048 A121049 A121050 * A121052 A121053 A121054

Keyword

easy,nonn,less

Author

Jonathan Vos Post, Aug 08 2006

Extensions

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

Status

approved