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

1,2

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Sequence in context: A104706 A366796 A094137 * A092942 A229137 A358631

Adjacent sequences: A038799 A038800 A038801 * A038803 A038804 A038805

Keyword

nonn

Author

Thomas Kellar

Extensions

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

Status

approved