OFFSET
0,6
COMMENTS
FORMULA
G.f.: (Sum_{primes p>=5} x^((p^2-1)/24))^4 = (Sum_{k>=3} x^A024702(k))^4.
EXAMPLE
100 = 5^2 + 5^2 + 5^2 + 5^2 (1 permutation).
124 = 5^2 + 5^2 + 5^2 + 7^2 (4 permutations).
148 = 5^2 + 5^2 + 7^2 + 7^2 (6 permutations).
172 = 5^2 + 7^2 + 7^2 + 7^2 (4 permutations).
196 = 7^2 + 7^2 + 7^2 + 7^2 (1 permutation) = 5^2 + 5^2 + 5^2 + 11^2 (4 permutations).
220 = 5^2 + 5^2 + 7^2 + 11^2 (12 permutations).
244 = 5^2 + 7^2 + 7^2 + 11^2 (12 permutations) = 5^2 + 5^2 + 5^2 + 13^2 (4 permutations).
268 = 7^2 + 7^2 + 7^2 + 11^2 (4 permutations) = 5^2 + 5^2 + 7^2 + 13^2 (12 permutations).
...
PROG
(PARI) a(n) = if(n<4, 0, polcoeff(sum(p=5, sqrt(24*n-48), if(isprime(p), x^((p^2-1)/24), 0))^4, n))
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, Jan 05 2019
STATUS
approved