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

1,4

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)

Links

Table of n, a(n) for n=1..50.

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)

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 *)

Crossrefs

Cf. A008578, A065475.

Sequence in context: A030543 A214084 A114143 * A359740 A171463 A020705

Adjacent sequences: A171523 A171524 A171525 * A171527 A171528 A171529

Keyword

nonn,easy

Author

Jaroslav Krizek, Dec 11 2009

Extensions

Corrected by Jaroslav Krizek, Dec 16 2009

Status

approved