cp's OEIS Frontend

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.

%I A287965 #16 Oct 14 2024 23:57:47
%S A287965 4,410,1014,1494,1685,2188,2335,2573,2717,2863,3054,3389,3224,3654,
%T A287965 3534,4014,4232,4183,4254,4064,4589,4618,4544,4593,4903,5193,5503,
%U A287965 5215,5579,5433,5455,5673,5962,5983,6158,6178,5744,5864,5984,5913,6223,6273,6678,6393,6442,6513,6870,6535,7038,7015
%N 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.
%C A287965 It appears that 1275 is the first k for which a(k) = 0. - _Robert Israel_, Oct 14 2024
%H A287965 Robert Israel, <a href="/A287965/b287965.txt">Table of n, a(n) for n = 1..1274</a>
%H A287965 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A287965 A111900(a(n)) = n.
%e A287965 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.
%p A287965 N:= 100: # to try with primes up to N
%p A287965 P:= select(isprime, [2,seq(i,i=3..N,2)]):
%p A287965 nP:= nops(P):
%p A287965 S:= mul(1+x^(P[i]^2), i=1..nP):
%p A287965 M:= 100: # for a(1) .. a(M)
%p A287965 V:= Vector(M): count:= 0:
%p A287965 for i from 4 to N^2 while count < M do
%p A287965   r:= coeff(S,x,i);
%p A287965   if r >= 1 and r <= M and V[r] = 0 then count:= count+1; V[r]:= i; fi
%p A287965 od:
%p A287965 convert(V,list); # _Robert Israel_, Oct 14 2024
%Y A287965 Cf. A001248, A048261, A097563, A111900, A121518.
%K A287965 nonn
%O A287965 1,1
%A A287965 _Ilya Gutkovskiy_, Jun 03 2017