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A120048 Number of 7-almost primes less than or equal to 10^n. 10

%I #8 Jan 25 2013 14:16:25

%S 0,0,0,14,231,2973,35585,409849,4600247,50678212,550454756,5913771637,

%T 62981797962,665997804082,7001087934965

%N Number of 7-almost primes less than or equal to 10^n.

%e There are 14 seven-almost primes up to 1000: 128, 192, 288, 320, 432, 448, 480, 648, 672, 704, 720, 800, 832 & 972.

%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 Table[AlmostPrimePi[7, 10^n], {n, 11}]

%Y Cf. A066265, A014613, A116382.

%Y Cf. A006880, A036352, A109251, A114106, A114453, A120047, A120048, A120049, A120050, A120051, A120052, A120053, A116430.

%K nonn

%O 0,4

%A _Robert G. Wilson v_, Feb 07 2006

%E More terms from _Robert G. Wilson v_, Jan 07 2007

%E Example corrected by _Harvey P. Dale_, Jan 25 2013

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Last modified March 19 06:32 EDT 2024. Contains 370953 sequences. (Running on oeis4.)