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A116434 Consider the array T(r,c), the number of c-almost primes less than or equal to r^c. This is the diagonal T(r,r-1). 1

%I #16 Oct 13 2023 11:46:53

%S 0,1,3,13,90,726,7089,78369,973404,13377156,201443165,3297443264,

%T 58304208767,1107693755122

%N Consider the array T(r,c), the number of c-almost primes less than or equal to r^c. This is the diagonal T(r,r-1).

%t AlmostPrimePi[k_Integer, n_] := Module[{a, i}, a[0] = 1; If[k == 1, PrimePi[n], Sum[PrimePi[n/Times @@ Prime[Array[a, k - 1]]] - a[k - 1] + 1, Evaluate[ Sequence @@ Table[{a[i], a[i - 1], PrimePi[(n/Times @@ Prime[Array[a, i - 1]])^(1/(k - i + 1))]}, {i, k - 1}]] ]]]; (* _Eric W. Weisstein_ Feb 07 2006 *)

%t Do[ Print@ AlmostPrimePi[n, (n + 1)^n], {n, 11}]

%Y Cf. A116433, A116435.

%K hard,more,nonn

%O 1,3

%A _Paul D. Hanna_ and _Robert G. Wilson v_, Feb 15 2006

%E Rephrased NAME. - _R. J. Mathar_, Jun 20 2021

%E a(13)-a(14) from _Max Alekseyev_, Oct 12 2023

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Last modified April 12 09:46 EDT 2024. Contains 371627 sequences. (Running on oeis4.)