cp's OEIS Frontend

A114989 Numbers whose sum of squares of distinct prime factors is prime.

%I A114989 #11 Jan 16 2016 11:41:48
%S A114989 6,10,12,14,18,20,24,26,28,34,36,40,48,50,52,54,56,68,72,74,80,94,96,
%T A114989 98,100,104,105,108,112,134,136,144,146,148,160,162,188,192,194,196,
%U A114989 200,206,208,216,224,231,250,268,272,273,274,288,292,296,315,320,324,326
%N A114989 Numbers whose sum of squares of distinct prime factors is prime.
%C A114989 A005063 is "sum of squares of primes dividing n." Hence this is the sum of squares of prime factors analog of A114522 "numbers n such that sum of distinct prime divisors of n is prime." Note the distinction between A005063 and A067666 is "sum of squares of prime factors of n (counted with multiplicity)."
%H A114989 Charles R Greathouse IV, <a href="/A114989/b114989.txt">Table of n, a(n) for n = 1..10000</a>
%F A114989 {k such that A005063(k) is prime}. {k such that A005063(k) is an element of A000040}. {k = (for distinct i, j, ... prime(i)^e_1 * prime(j)^e_2 * ...) such that (prime(i)^2 * prime(j)^2 * ...) is prime}.
%e A114989 a(1) = 6 because 6 = 2 * 3 and 2^2 + 3^2 = 13 is prime.
%e A114989 a(2) = 10 because 10 = 2 * 5 and 2^2 + 5^2 = 29 is prime.
%e A114989 a(3) = 12 because 12 = 2^2 * 3 and 2^2 + 3^2 = 13 is prime (note that we are not counting the prime factors with multiplicity).
%e A114989 a(4) = 14 because 14 = 2 * 7 and 2^2 + 7^2 = 53 is prime.
%e A114989 a(8) = 26 because 26 = 2 * 3 and 2^2 + 13^2 = 173 is prime.
%e A114989 a(10) = 34 because 34 = 2 * 17 and 2^2 + 17^2 = 293 is prime.
%p A114989 with(numtheory): a:=proc(n) local DPF: DPF:=factorset(n): if isprime(sum(DPF[j]^2,j=1..nops(DPF)))=true then n else fi end: seq(a(n),n=1..400); # _Emeric Deutsch_, Mar 07 2006
%t A114989 Select[Range[400],PrimeQ[Total[Transpose[FactorInteger[#]][[1]]^2]]&] (* _Harvey P. Dale_, Jan 16 2016 *)
%o A114989 (PARI) is(n)=isprime(norml2(factor(n)[,1]))
%Y A114989 Cf. A005063, A067666, A014612, A014613, A069273, A069279, A069281, A114522.
%K A114989 easy,nonn
%O A114989 1,1
%A A114989 _Jonathan Vos Post_, Feb 22 2006
%E A114989 More terms from _Emeric Deutsch_, Mar 07 2006