OFFSET
1,1
COMMENTS
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)."
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
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.
MAPLE
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
MATHEMATICA
Select[Range[400], PrimeQ[Total[Transpose[FactorInteger[#]][[1]]^2]]&] (* Harvey P. Dale, Jan 16 2016 *)
PROG
(PARI) is(n)=isprime(norml2(factor(n)[, 1]))
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 22 2006
EXTENSIONS
More terms from Emeric Deutsch, Mar 07 2006
STATUS
approved