A071571 Smallest number whose square has exactly 2n+1 divisors.

1, 2, 4, 8, 6, 32, 64, 12, 256, 512, 24, 2048, 36, 30, 16384, 32768, 96, 72, 262144, 192, 1048576, 2097152, 60, 8388608, 216, 768, 67108864, 288, 1536, 536870912, 1073741824, 120, 576, 8589934592, 6144, 34359738368, 68719476736, 180, 864

Offset

0,2

Comments

Only squares have an odd number of divisors.

Links

Amiram Eldar, Table of n, a(n) for n = 0..3325

Formula

a(n) <= 2^n, where the equality holds if and only if n=0 or 2n+1 is prime. - Jianing Song, Aug 30 2021

Example

a(4)=6 because it is the smallest number followed by 10,14,15,16,21,22,... whose squares have 2*4 + 1, i.e., 9 divisors.

Prog

(PARI) a(n) = {k = 1; while (numdiv(k^2) != (2*n+1), k++); return (k); } \\ Michel Marcus, Jul 27 2013

Crossrefs

Cf. A005179.

Identical to A016017 shifted left.

Sequence in context: A328964 A061284 A016017 * A201568 A029898 A153130

Adjacent sequences: A071568 A071569 A071570 * A071572 A071573 A071574

Keyword

nonn,changed

Author

Lekraj Beedassy, May 31 2002

Extensions

More terms from Vladeta Jovovic, Jun 05 2002

a(0) prepended by Jianing Song, Aug 30 2021

Status

approved