A120046 The 10^n-th 5-almost prime.

32, 176, 1272, 10374, 89896, 810220, 7475818, 70185558, 667561977, 6411296283, 62037096770, 603813941738

Offset

0,1

Links

Table of n, a(n) for n=0..11.

Formula

a(n) = A014614(10^n). - Amiram Eldar, Apr 29 2024

Mathematica

FiveAlmostPrimePi[n_] := Sum[ PrimePi[n/(Prime@i*Prime@j*Prime@k*Prime@l)] - l + 1, {i, PrimePi[n^(1/5)]}, {j, i, PrimePi[(n/Prime@i)^(1/4)]}, {k, j, PrimePi[(n/(Prime@i*Prime@j)^(1/3))]}, {l, k, PrimePi@Sqrt[(n/(Prime@i*Prime@j*Prime@k))]}];
FiveAlmostPrime[n_] := Block[{e = Floor[Log[2, n] +4], a, b}, a = 2^e; Do[b = 2^p; While[FiveAlmostPrimePi[a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; Do[ Print@FiveAlmostPrime[10^n], {n, 0, 13}]

Prog

(PARI) lista(nmax) = {my(pow = 1, c = 0, n = 0); for(k = 1, oo, if(bigomega(k) == 5, c++; if(c == pow, print1(k, ", "); if(n == nmax, break); pow *= 10; n++))); } \\ Amiram Eldar, Apr 29 2024

Crossrefs

Cf. A014614, A114453, A006988, A114125, A120044, A120045.

Sequence in context: A181209 A231299 A029534 * A370649 A303798 A305243

Adjacent sequences: A120043 A120044 A120045 * A120047 A120048 A120049

Keyword

nonn,hard,more

Author

Robert G. Wilson v, Feb 15 2006

Extensions

a(6) corrected and a(7)-a(9) added by Amiram Eldar, Apr 29 2024

a(10)-a(11) from David A. Corneth, Apr 29 2024

Status

approved