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A071571 Smallest number whose square has exactly 2n+1 divisors. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Only squares have an odd number of divisors.

LINKS

Table of n, a(n) for n=0..38.

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

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

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Last modified November 28 04:13 EST 2021. Contains 349400 sequences. (Running on oeis4.)