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A078845 Where 7^n occurs in n-almost-primes, starting at a(0)=1. 12
1, 4, 17, 82, 385, 1688, 7089, 28893, 115180, 450906, 1740244, 6640747, 25115604, 94312569, 352110321, 1308256678, 4841115048, 17852264639, 65636109307, 240689877440, 880582139867 (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..20.

Eric Weisstein's World of Mathematics, Almost Prime.

EXAMPLE

a(2) = 17 since 7^2 is the 17th 2-almost-prime: {4,6,9,10,14,15,21,22,25,26,33,34,35,38,39,46,49,...}.

MATHEMATICA

l = Table[0, {30}]; e = 0; Do[f = Plus @@ Last /@ FactorInteger[n]; l[[f+1]]++; If[n == 7^e, Print[l[[f+1]]]; e++ ], {n, 1, 7^10}] (* Ryan Propper, Aug 08 2005 *)

AlmostPrimePi[k_Integer /; k > 1, n_] := Module[{a, i}, a[0] = 1; 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, 7^n], {n, 2, 15}] (* Robert G. Wilson v, Feb 09 2006 *)

CROSSREFS

Cf. A078840, A078841, A078842, A078843, A078844, A078846.

Sequence in context: A151250 A174810 A121545 * A230126 A181517 A110771

Adjacent sequences:  A078842 A078843 A078844 * A078846 A078847 A078848

KEYWORD

nonn

AUTHOR

Benoit Cloitre and Paul D. Hanna, Dec 10 2002

EXTENSIONS

a(7)-a(10) from Ryan Propper, Aug 08 2005

a(11)-a(15) from Robert G. Wilson v, Feb 09 2006

a(16)-a(20) from Donovan Johnson, Sep 27 2010

STATUS

approved

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Last modified January 18 05:18 EST 2021. Contains 340250 sequences. (Running on oeis4.)