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A078844 Where 5^n occurs in n-almost-primes, starting at a(0)=1. 14
1, 3, 9, 30, 90, 269, 788, 2249, 6340, 17526, 47911, 129639, 348251, 929714, 2469499, 6532869, 17219031, 45246630, 118572805, 309998131, 808746993, 2105893899, 5474080107, 14207001052, 36818679828, 95292132897, 246327403310 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..26.

Eric Weisstein's World of Mathematics, Almost Prime.

EXAMPLE

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

MATHEMATICA

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 *)

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 *)

Table[ AlmostPrimePi[n, 5^n], {n, 2, 25}] (* Robert G. Wilson v *)

CROSSREFS

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

Sequence in context: A179545 A163129 A074003 * A144817 A337267 A337034

Adjacent sequences:  A078841 A078842 A078843 * A078845 A078846 A078847

KEYWORD

nonn

AUTHOR

Benoit Cloitre and Paul D. Hanna, Dec 10 2002

EXTENSIONS

a(8)-a(10) from Ryan Propper, Aug 08 2005

a(11)-a(25) from Robert G. Wilson v, Feb 10 2006

a(26) from Donovan Johnson, Sep 27 2010

STATUS

approved

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Last modified January 22 03:32 EST 2021. Contains 340360 sequences. (Running on oeis4.)