A171526 Denominator of (n-th noncomposite/n).

1, 1, 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50

Offset: 1

Author

Jaroslav Krizek, Dec 11 2009

Keywords

• nonn
• easy

Comments

Denominator of (A008578(n)/n).

From Enrique Navarrete, Mar 15 2025: (Start)

a(n+1) is the number of binary strings of length n with at most one 0 and either zero or at least two 1s. For example, for n=2, a(3)=1 since the string is 11; for n=3, a(4)=4 since the strings are 111, 011, 101, 110.

a(n+1) is also the number of ordered set partitions of an n-set into 2 sets such that the first set is empty or has one element and the second set is empty or has at least two elements. (End)

Crossrefs

Cf. A008578, A065475.

Programs

Mathematica

Module[{nn=300,c,len},c=Select[Range[nn],!CompositeQ[#]&];len=Length[ c]; #[[1]]/#[[2]]&/@Thread[{c,Range[len]}]]//Denominator (* or *) Join[{1,1,1}, Range[ 4,60]] (* Harvey P. Dale, Feb 08 2020 *)

Formula

a(1) = a(2) = a(3) = 1, a(n) = n for n >= 4.

From Enrique Navarrete, Mar 15 2025: (Start)

G.f.: x*(1-x+3*x^3-2*x^4)/(1-x)^2.

E.g.f.: x*exp(x)-x^2/2-x^3/3. (End)

Extensions

Corrected by Jaroslav Krizek, Dec 16 2009