A078846 Where 11^n occurs in n-almost-primes, starting at a(0)=1.

1, 5, 40, 328, 2556, 18452, 126096, 827901, 5276913, 32887213, 201443165, 1217389949, 7279826998, 43168558912, 254258462459, 1489291941733, 8683388113017, 50433408838966

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..17.

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, Feb 09 2006 *)

Prog

(PARI)
almost_prime_count(N, k) = if(k==1, return(primepi(N))); (f(m, p, k, j=0) = my(c=0, s=sqrtnint(N\m, k)); if(k==2, forprime(q=p, s, c += primepi(N\(m*q))-j; j += 1), forprime(q=p, s, c += f(m*q, q, k-1, j); j += 1)); c); f(1, 2, k);
a(n) = if(n == 0, 1, almost_prime_count(11^n, n)); \\ Daniel Suteu, Jul 10 2023

Crossrefs

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

Sequence in context: A123943 A067412 A355355 * 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

a(16)-a(17) from Daniel Suteu, Jul 10 2023

Status

approved