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a(n) is the index of the n-th compositorial number, A036691(n), in the sequence of composites (A002808).
1

%I #26 Jun 02 2021 22:38:16

%S 1,14,148,1458,15293,188782,2692726,40909988,660637057,11976280879,

%T 240871231369,5080851687840,112183659405198,2700581280109040,

%U 67686358108129808,1763651979163805444,47707175694652299653,1337959106215345951164,40196133912310028013721,1287910861213828031657392

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

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

%F a(n) = A065855(A036691(n)). - _Chai Wah Wu_, Sep 08 2020

%e 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.

%t Table[A036691[n]-(PrimePi[A036691[n]])-1, {n, 1, 9}]

%t 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} ]

%o (Python)

%o from sympy import factorial, primepi, composite, primorial, compositepi

%o def A065899(n):

%o return compositepi(factorial(composite(n))//primorial(primepi(composite(n)))) # _Chai Wah Wu_, Sep 08 2020

%Y Cf. A002808, A000720, A036691, A065855.

%K nonn

%O 1,2

%A _Labos Elemer_, Nov 28 2001

%E One more term from _Robert G. Wilson v_, Nov 29 2001

%E a(11)-a(19) from _Chai Wah Wu_, Sep 08 2020

%E a(20) from _Chai Wah Wu_, Sep 09 2020

%E Name rewritten by _Felix Fröhlich_, Jun 01 2021