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A122942 Partial product of n-th n-almost prime (A101695) divided by product of the first n primes, rounded down. 1
1, 2, 7, 41, 403, 6960, 196527, 13405218, 1566662070, 304256578608, 113065670502087, 78229220671714544, 101598769325059903837, 293965406612712860369329, 1613982664799943153033715558 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..15.

FORMULA

a(n) = floor((Prod[i=1..n] i-th i-almost prime)/A002110(i)) = floor(Prod[i=1..n] A101695(i)/A000040(i)).

EXAMPLE

a(1) = floor(2/2) = floor(1) = 1.

a(2) = floor(12/6) = floor(2) = 2.

a(3) = floor(216/30) = floor(7.2) = 7.

a(4) = floor(8640/210) = floor(41.1428571) = 41.

a(5) = floor(933120/2310) = floor(403.948052) = 403.

a(6) = floor(209018880/30030) = floor(6960.33566) = 6960.

a(7) = floor(100329062400/510510) = floor(196527.125) = 196527.

a(8) = floor(130026464870400/9699690) = floor(13405218.6) = 13405218.

a(9) = floor(349511137571635200/223092870) = floor(1566662070.247) = 1566662070.

a(10) = floor(1968446726803449446400/6469693230) = floor(304256578608.0478) = 304256578608.

a(11) = floor(22676506292775737622528000/200560490130) = floor(113065670502087.42) = 113065670502087.

a(12) = floor(522466704985552994823045120000/7420738134810) = 70406298604543089.

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 *)

AlmostPrime[k_, n_] := Block[{e = Floor[Log[2, n]+k], a, b}, a = 2^e; Do[b = 2^p; While[ AlmostPrimePi[k, a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; AlmostPrime[1, 1] = 2; - Robert G. Wilson v, Aug 31 2007

t = Table[ AlmostPrime[n, n], {n, 20}]; Floor[Rest@ FoldList[Times, 1, t]/Rest@ FoldList[Times, 1, Prime@ Range@ 20]] - Robert G. Wilson v, Aug 31 2007

CROSSREFS

Cf. A000040, A001222, A002110, A008587, A101695, A008585, A014613, A014614, A086046, A086047, A112141, A114426, A122093, A122609.

Sequence in context: A213434 A008934 A084871 * A159315 A191601 A265772

Adjacent sequences:  A122939 A122940 A122941 * A122943 A122944 A122945

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Oct 24 2006

EXTENSIONS

More terms from Robert G. Wilson v, Aug 31 2007

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)