

A183168


Number of partitions of n^2 into three distinct primes.


3



0, 0, 0, 1, 2, 3, 8, 2, 17, 3, 41, 7, 61, 6, 69, 8, 152, 11, 216, 6, 204, 10, 383, 16, 464, 14, 447, 14, 791, 18, 978, 18, 822, 18, 1302, 25, 1684, 27, 1387, 24, 2347, 28, 2726, 27, 2012, 34, 3620, 31, 4005, 32, 3218, 44, 5274, 44, 5461, 36, 4538, 43, 7429
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OFFSET

1,5


COMMENTS

For n>3, odd n have (many) more partitions than even n.


LINKS

Zak Seidov, Table of n, a(n) for n = 1..200


EXAMPLE

a(4)=1 because 16=2+3+11,
a(6)=3 because 36=2+3+31=2+5+29=2+11+13.


MATHEMATICA

Table[Count[Union/@IntegerPartitions[n^2, {3}], _?(Length[#]==3&&AllTrue[ #, PrimeQ]&)], {n, 60}] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 02 2018 *)


PROG

(PARI) a(n)=my(s); n*=n; forprime(p=n\3, n4, forprime(q=(np)\2+1, min(np, p1), if(isprime(npq), s++))); s \\ Charles R Greathouse IV, Aug 27 2012
(Haskell)
a183168 n = z (drop (fromInteger (mod n 2)) a000040_list) (n ^ 2) 3 where
z _ m 1 = if m <= 0 then 0 else a010051 m
z (p:ps) m c = if m <= 2*p then 0 else z ps (m  p) (c  1) + z ps m c
 Reinhard Zumkeller, Aug 28 2012


CROSSREFS

Subsequence of A125688: a(n) = A125688(n^2).
Cf. A215933, A215934.
Cf. A000040, A010051.
Sequence in context: A252651 A058485 A204907 * A011326 A154826 A155994
Adjacent sequences: A183165 A183166 A183167 * A183169 A183170 A183171


KEYWORD

nonn


AUTHOR

Zak Seidov, Aug 27 2012


STATUS

approved



