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.

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

Author

Ilya Gutkovskiy, Jun 03 2017

Keywords

• nonn

Comments

It appears that 1275 is the first k for which a(k) = 0. - Robert Israel, Oct 14 2024

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1274
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A001248, A048261, A097563, A111900, A121518.

Programs

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

Formula

A111900(a(n)) = n.