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 A103558 Semiprimes of the form p^2 + q^2, where p and q are primes. 2
 34, 58, 74, 146, 178, 194, 218, 298, 314, 365, 386, 458, 482, 533, 538, 554, 698, 818, 866, 965, 1082, 1202, 1322, 1418, 1538, 1658, 1685, 1706, 1853, 1858, 1874, 2018, 2042, 2138, 2218, 2234, 2258, 2498, 2642, 2813, 2818, 2858, 2978, 3098, 3218, 3338 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS p and q must be distinct, otherwise p^2 + q^2 = 2*p*p has three prime factors. - Klaus Brockhaus Even terms are 2*A103739. - Robert Israel, Nov 03 2017 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 34 is a term because 3^2 + 5^2 = 34 = 2*17; 58 is a term because 3^2 + 7^2 = 58 = 2*29; 74 is a term because 5^2 + 7^2 = 74 = 2*37. MAPLE N:= 10000: # to get all terms <= N P:= select(isprime, [\$1..floor(sqrt(N))]): Res:= NULL: for i from 1 to nops(P) do   for j from 1 to i-1 do     r:= P[i]^2 + P[j]^2;     if r > N then break fi;     if numtheory:-bigomega(r) = 2 then Res:= Res, r fi; od od: sort(convert({Res}, list)); # Robert Israel, Nov 03 2017 MATHEMATICA fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; Select[ Sort[ Flatten[ Table[ Prime[p]^2 + Prime[q]^2, {p, 16}, {q, p - 1}]]], fQ[ # ] &] (* Robert G. Wilson v, Mar 23 2005 *) PROG (PARI) {m=53; v=[]; forprime(p=2, m, forprime(q=nextprime(p+1), m, if(bigomega(k=p^2+q^2)==2, v=concat(v, k)))); v=vecsort(v); stop=nextprime(m+1)^2; for(j=1, length(v), if(v[j]

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Last modified December 16 09:34 EST 2018. Contains 318160 sequences. (Running on oeis4.)