1,1

A005063 is "sum of squares of primes dividing n." Hence this is the sum of squares of prime factors analogue 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)."

{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}.

a(1) = 6 because 6 = 2 * 3, and 2^2 + 3^2 = 13 is prime.

a(2) = 10 because 10 = 2 * 5, and 2^2 + 5^2 = 29 is prime.

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).

a(4) = 14 because 14 = 2 * 7, and 2^2 + 7^2 = 53 is prime.

a(8) = 26 because 26 = 2 * 3, and 2^2 + 13^2 = 173 is prime.

a(10) = 34 because 34 = 2 * 17, and 2^2 + 17^2 = 293 is prime.

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 (deutsch(AT)duke.poly.edu), Mar 07 2006

Cf. A005063, A067666, A014612, A014613, A069273, A069279, A069281, A114522.

Sequence in context: A054741 A098902 A100367 this_sequence A129493 A036350 A088829

Adjacent sequences: A114986 A114987 A114988 this_sequence A114990 A114991 A114992

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 22 2006

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 07 2006