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A287965
Smallest number which can be represented as the sum of distinct squares of primes in exactly n ways, or 0 if no such integer exists.
2
4, 410, 1014, 1494, 1685, 2188, 2335, 2573, 2717, 2863, 3054, 3389, 3224, 3654, 3534, 4014, 4232, 4183, 4254, 4064, 4589, 4618, 4544, 4593, 4903, 5193, 5503, 5215, 5579, 5433, 5455, 5673, 5962, 5983, 6158, 6178, 5744, 5864, 5984, 5913, 6223, 6273, 6678, 6393, 6442, 6513, 6870, 6535, 7038, 7015
OFFSET
1,1
COMMENTS
It appears that 1275 is the first k for which a(k) = 0. - Robert Israel, Oct 14 2024
FORMULA
A111900(a(n)) = n.
EXAMPLE
a(2) = 410 because 410 = 7^2 + 19^2 = 11^2 + 17^2 and this is the smallest number that can be written as the sum of distinct squares of primes in 2 different ways.
MAPLE
N:= 100: # to try with primes up to N
P:= select(isprime, [2, seq(i, i=3..N, 2)]):
nP:= nops(P):
S:= mul(1+x^(P[i]^2), i=1..nP):
M:= 100: # for a(1) .. a(M)
V:= Vector(M): count:= 0:
for i from 4 to N^2 while count < M do
r:= coeff(S, x, i);
if r >= 1 and r <= M and V[r] = 0 then count:= count+1; V[r]:= i; fi
od:
convert(V, list); # Robert Israel, Oct 14 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 03 2017
STATUS
approved