The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A117526 Least number a(n) which is a product of n primes and such that Pi_n(a(n))/a(n) is maximum. 1
 3, 10, 9837, 259441550133 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Pi_n(a(n))/a(n): 0.66667, 0.40000, 0.25801, 0.2145967653 3=3, 10=2*5, 9837=3*3*1093 & 259441550133=3*89*311*3124409. 3 is the second prime, 10 is the fourth semiprime, 9837 is the 3-almost prime, and 259441550133 is the 4-almost prime. LINKS Eric Weisstein's World of Mathematics, Almost Prime. Eric Weisstein's World of Mathematics, Prime Factor. EXAMPLE a(1)=3 because Pi(2)/2=1/2 < Pi(3)/3=2/3 > Pi(5)/5=3/5. a(2)=10 because Pi_2(9)/9=1/3 < Pi_2(10)/10=2/5 > Pi_2(14)/14=5/14; Pi_2(10)/10 = Pi_2(15)/15 but 10 < 15. 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 *) fQ[n_] := Plus @@ Last /@ FactorInteger@n == 4; c = r = 0; Do[If[fQ@n, c++ ]; If[c/n > r, Print[n]; r = c/n], {n, 10^6}] CROSSREFS Cf. A006880, A066265, A109251, A114106, A114453. Sequence in context: A202712 A006273 A183130 * A051498 A092528 A069604 Adjacent sequences:  A117523 A117524 A117525 * A117527 A117528 A117529 KEYWORD nonn AUTHOR Martin Raab and Robert G. Wilson v, Mar 25 2006 EXTENSIONS Comment edited and a(4) added by Donovan Johnson, Mar 10 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 5 06:46 EDT 2020. Contains 336209 sequences. (Running on oeis4.)