A192861 Flat numbers: odd n such that n+1 is a squarefree number times a power of two.

1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 25, 27, 29, 31, 33, 37, 39, 41, 43, 45, 47, 51, 55, 57, 59, 61, 63, 65, 67, 69, 73, 75, 77, 79, 81, 83, 85, 87, 91, 93, 95, 101, 103, 105, 109, 111, 113, 115, 117, 119, 121, 123, 127, 129, 131, 133, 135, 137, 139, 141

Offset: 1

Author

Charles R Greathouse IV, Jul 11 2011

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Kevin Broughan and Zhou Qizhi, Flat primes and thin primes, Bulletin of the Australian Mathematical Society 82:2 (2010), pp. 282-292.

Crossrefs

Cf. A192862.

Programs

PARI

is(n)=n%2&&issquarefree((n+1)>>valuation(n+1,2))

PARI

list(lim)=my(v=List()); for(k=1,logint(1+lim\=1,2), forsquarefree(n=1,(lim+1)>>k, listput(v, n[1]<Charles R Greathouse IV, Mar 01 2018

Formula

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