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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
 0, 1, 3, 13, 90, 726, 7089, 78369, 973404, 13377156, 201443165, 3297443264, 58304208767, 1107693755122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..14. MATHEMATICA 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 *) Do[ Print@ AlmostPrimePi[n, (n + 1)^n], {n, 11}] CROSSREFS Cf. A116433, A116435. Sequence in context: A097711 A114477 A345104 * A174290 A034513 A257661 Adjacent sequences: A116431 A116432 A116433 * A116435 A116436 A116437 KEYWORD hard,more,nonn AUTHOR Paul D. Hanna and Robert G. Wilson v, Feb 15 2006 EXTENSIONS Rephrased NAME. - R. J. Mathar, Jun 20 2021 a(13)-a(14) from Max Alekseyev, Oct 12 2023 STATUS approved

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Last modified March 4 23:31 EST 2024. Contains 370537 sequences. (Running on oeis4.)