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A078846 Where 11^n occurs in n-almost-primes, starting at a(0)=1. 14
1, 5, 40, 328, 2556, 18452, 126096, 827901, 5276913, 32887213, 201443165, 1217389949, 7279826998, 43168558912, 254258462459, 1489291941733 (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..15.

Eric Weisstein's World of Mathematics, Almost Prime.

EXAMPLE

a(2) = 40 since 11^2 is the 40th 2-almost-prime: A001358(40) = 121.

MATHEMATICA

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, 11^n], {n, 2, 11}] (* Robert G. Wilson v *)

CROSSREFS

Cf. A078840, A078841, A078842, A078843, A078844, A078845.

Sequence in context: A145841 A123943 A067412 * A027259 A007036 A264227

Adjacent sequences:  A078843 A078844 A078845 * A078847 A078848 A078849

KEYWORD

more,nonn

AUTHOR

Benoit Cloitre and Paul D. Hanna, Dec 10 2002

EXTENSIONS

a(6)-a(11) from Robert G. Wilson v, Feb 09 2006

a(12)-a(15) 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.)