A045698 - OEIS

A045698

Number of ways n can be written as the sum of two squares of primes.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,339

COMMENTS

a(A214879(n)) = 0; a(A045636(n)) > 0; a(A214723(n)) = 1; a(A214511(n)) = n and a(m) < n for m < A214511(n). - Reinhard Zumkeller, Jul 29 2012

The smallest value of n such that a(n) = 2 is 338. (This helps distinguish it from the characteristic function of A045636.) - Wesley Ivan Hurt, Jun 13 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for sequences related to sums of squares

EXAMPLE

For example, a(29) = 1 because 29 = 2^2 + 5^2. a(3) = 0 because there is no way to write 3 as sum of two squares of primes.

PROG

(Haskell)

a045698 n = length $ filter (\x -> x > 0 && a010051' x == 1) $

map (a037213 . (n -)) $

takeWhile (<= div n 2) a001248_list

-- Reinhard Zumkeller, Jul 29 2012

(PARI) a(n)=my(s=0, q); forprime(p=2, sqrtint(n\2), if(issquare(n-p^2, &q)&&isprime(q), s++)); s \\ Charles R Greathouse IV, Jun 04 2014