A192863 Lower flat numbers: odd numbers k such that k-1 is a squarefree number times a power of two.

3, 5, 7, 9, 11, 13, 15, 17, 21, 23, 25, 27, 29, 31, 33, 35, 39, 41, 43, 45, 47, 49, 53, 57, 59, 61, 63, 65, 67, 69, 71, 75, 77, 79, 81, 83, 85, 87, 89, 93, 95, 97, 103, 105, 107, 111, 113, 115, 117, 119, 121, 123, 125, 129, 131, 133, 135, 137, 139, 141, 143, 147

Offset: 1

Author

Charles R Greathouse IV, Jul 11 2011

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Kevin A. Broughan and Zhou Qizhi, Flat primes and thin primes, Bulletin of the Australian Mathematical Society, Vol. 82, No. 2 (2010), pp. 282-292, alternative link.

Crossrefs

Cf. A192861, A192862, A192864.

Cf. A185199 (asymptotic density of this sequence).

Programs

Mathematica

Select[Range[3, 150, 2], SquareFreeQ[(# - 1)/2^IntegerExponent[# - 1, 2]] &] (* Amiram Eldar, Aug 30 2020 *)

PARI

is(n)=n%2&&issquarefree((n-1)>>valuation(n-1,2)) \\ corrected by Amiram Eldar, Aug 30 2020

Formula

a(n) ~ Pi^2/4 * n.

Extensions

Data corrected by Amiram Eldar, Aug 30 2020