A392801 Integers k such that the sum of the first k squarefree numbers is a square.

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..13.

Formula

A173143(a(n)) = A262783(n). - Amiram Eldar, Jan 23 2026

Example

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.

Prog

(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

Crossrefs

Cf. A005117, A173143, A262783.

Sequence in context: A321941 A116343 A259473 * A202785 A255535 A034544

Adjacent sequences: A392798 A392799 A392800 * A392802 A392803 A392804

Keyword

nonn,more

Author

Gonzalo Martínez, Jan 23 2026

Extensions

a(12)-a(13) from Amiram Eldar, Jan 23 2026

Status

approved