A392801 - OEIS

%I #13 Jan 27 2026 19:09:30

%S 1,14,87,204,215,2771,3514,4224,4933,63269,219430,335247600,1861405559

%N Integers k such that the sum of the first k squarefree numbers is a square.

%C If A173143(k) is a square, then k is a term of the sequence.

%F A173143(a(n)) = A262783(n). - _Amiram Eldar_, Jan 23 2026

%e The first 14 squarefree integers are 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21 whose sum is 144 = 12^2. So, 14 is a term.

%o (PARI) list(lim) = my(sm = 0, n = 0); forsquarefree(k = 1, lim\1, n++; sm += k[1]; if(issquare(sm), print1(n, ", "))); \\ _Amiram Eldar_, Jan 23 2026

%Y Cf. A005117, A173143, A262783.

%K nonn,more

%O 1,2

%A _Gonzalo Martínez_, Jan 23 2026

%E a(12)-a(13) from _Amiram Eldar_, Jan 23 2026