A287965 - OEIS

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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.

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

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OFFSET

1,1

COMMENTS

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

LINKS

Robert Israel, Table of n, a(n) for n = 1..1274

Index entries for sequences related to sums of squares

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