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A078844 Where 5^n occurs in n-almost-primes, starting at a(0)=1. 14

%I

%S 1,3,9,30,90,269,788,2249,6340,17526,47911,129639,348251,929714,

%T 2469499,6532869,17219031,45246630,118572805,309998131,808746993,

%U 2105893899,5474080107,14207001052,36818679828,95292132897,246327403310

%N Where 5^n occurs in n-almost-primes, starting at a(0)=1.

%C A k-almost-prime is a positive integer that has exactly k prime factors, counted with multiplicity.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostPrime.html">Almost Prime.</a>

%e a(2) = 9 since 5^2 is the 9th 2-almost-prime: {4,6,9,10,14,15,21,22,25,...}.

%t l = Table[0, {30}]; e = 0; Do[f = Plus @@ Last /@ FactorInteger[n]; l[[f+1]]++; If[n == 5^e, Print[l[[f+1]]]; e++ ], {n, 1, 5^10}] (* _Ryan Propper_, Aug 08 2005 *)

%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[n, 5^n], {n, 2, 25}] (* _Robert G. Wilson v_ *)

%Y Cf. A078840, A078841, A078842, A078843, A078845, A078846.

%K nonn

%O 0,2

%A _Benoit Cloitre_ and _Paul D. Hanna_, Dec 10 2002

%E a(8)-a(10) from _Ryan Propper_, Aug 08 2005

%E a(11)-a(25) from _Robert G. Wilson v_, Feb 10 2006

%E a(26) from _Donovan Johnson_, Sep 27 2010

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Last modified March 1 02:21 EST 2021. Contains 341732 sequences. (Running on oeis4.)