A038802 Factor 2n+1 = (2^m1)*(3^m2)*(5^m3)*...; a(n) = number of initial zero exponents.

1, 2, 3, 1, 4, 5, 1, 6, 7, 1, 8, 2, 1, 9, 10, 1, 2, 11, 1, 12, 13, 1, 14, 3, 1, 15, 2, 1, 16, 17, 1, 2, 18, 1, 19, 20, 1, 3, 21, 1, 22, 2, 1, 23, 3, 1, 2, 24, 1, 25, 26, 1, 27, 28, 1, 29, 2, 1, 3, 4, 1, 2, 30, 1, 31, 3, 1, 32, 33, 1, 4, 2, 1, 34, 35, 1, 2, 36

Offset: 1

Author

Thomas Kellar

Keywords

• nonn

Examples

			9 = (2^0)*(3^2), thus a(4) = 1.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Programs

Maple

A038802 := proc(n) numtheory[factorset](2*n+1) ; min(%); numtheory[pi](%)-1 ; end proc: # R. J. Mathar, Mar 01 2011

Mathematica

Table[f = FactorInteger[2 n + 1]; PrimePi[f[[1, 1]]] - 1, {n, 100}] (* T. D. Noe, Apr 23 2013 *)

PARI

lpf(n)=factor(n)[1,1]
a(n)=primepi(lpf(2*n+1))-1 \\ Charles R Greathouse IV, Jul 29 2016

Formula

a(n) = A049084(A020639(2n+1))-1. - R. J. Mathar, Mar 01 2011

Extensions

a(69) corrected by Rick G. Rosner, Apr 22 2013