A120046 - OEIS

%I #18 May 05 2024 07:59:36

%S 32,176,1272,10374,89896,810220,7475818,70185558,667561977,6411296283,

%T 62037096770,603813941738

%N The 10^n-th 5-almost prime.

%F a(n) = A014614(10^n). - _Amiram Eldar_, Apr 29 2024

%t 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))]}];

%t 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}]

%o (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

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

%K nonn,hard,more

%O 0,1

%A _Robert G. Wilson v_, Feb 15 2006

%E a(6) corrected and a(7)-a(9) added by _Amiram Eldar_, Apr 29 2024

%E a(10)-a(11) from _David A. Corneth_, Apr 29 2024