A065899 a(n) is the index of the n-th compositorial number, A036691(n), in the sequence of composites (A002808).

1, 14, 148, 1458, 15293, 188782, 2692726, 40909988, 660637057, 11976280879, 240871231369, 5080851687840, 112183659405198, 2700581280109040, 67686358108129808, 1763651979163805444, 47707175694652299653, 1337959106215345951164, 40196133912310028013721, 1287910861213828031657392

Offset: 1

Author

Labos Elemer, Nov 28 2001

Keywords

• nonn

Examples

			a(2) = 14 because 4*6 = 24, the 2nd compositorial number is the 14th composite number: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24.
		

Crossrefs

Cf. A002808, A000720, A036691, A065855.

Programs

Mathematica

Table[A036691[n]-(PrimePi[A036691[n]])-1, {n, 1, 9}]
Composite[n_] := FixedPoint[n + PrimePi[ # ] + 1 &, n + PrimePi[n] + 1]; Table[c = Product[ Composite[i], {i, 1, n} ]; c - PrimePi[c] - 1, {n, 1, 10} ]

Python

from sympy import factorial, primepi, composite, primorial, compositepi
def A065899(n):
    return compositepi(factorial(composite(n))//primorial(primepi(composite(n)))) # Chai Wah Wu, Sep 08 2020

Formula

a(n) = A036691(n) - primepi(A036691(n))-1.

a(n) = A065855(A036691(n)). - Chai Wah Wu, Sep 08 2020

Extensions

One more term from Robert G. Wilson v, Nov 29 2001

a(11)-a(19) from Chai Wah Wu, Sep 08 2020

a(20) from Chai Wah Wu, Sep 09 2020

Name rewritten by Felix Fröhlich, Jun 01 2021