A120045 The (10^n)-th 4-almost prime.

16, 88, 693, 5958, 54328, 511725, 4922511, 47997635, 472514554, 4683086217, 46636297326, 466032880556, 4668833302876, 46861389462777

Offset

0,1

Links

Table of n, a(n) for n=0..13.

Formula

a(n) = A014613(10^n). - Chai Wah Wu, Jun 03 2026

Mathematica

FourAlmostPrimePi[n_] := Sum[ PrimePi[n/(Prime@i*Prime@j*Prime@k)] - k + 1, {i, PrimePi[n^(1/4)]}, {j, i, PrimePi[(n/Prime@i)^(1/3)]}, {k, j, PrimePi@Sqrt[n/(Prime@i*Prime@j)]}];
FourAlmostPrime[n_] := Block[{e = Floor[Log[2, n] +3], a, b}, a = 2^e; Do[b = 2^p; While[FourAlmostPrimePi[a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; Do[ Print@FourAlmostPrime[10^n], {n, 0, 11}]

Prog

(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot
from oeis_sequences.OEISsequences import bisection
def A120045(n):
    n10 = 10**n
    def f(x): return int(n10+x-sum(primepi(x//(k*m*r))-c for a, k in enumerate(primerange(integer_nthroot(x, 4)[0]+1)) for b, m in enumerate(primerange(k, integer_nthroot(x//k, 3)[0]+1), a) for c, r in enumerate(primerange(m, isqrt(x//(k*m))+1), b)))
    return bisection(f, n10, n10) # Chai Wah Wu, Jun 03 2026

Crossrefs

Cf. A006988, A014613, A114106, A114125, A120044, A120046.

Sequence in context: A035291 A358084 A309271 * A301794 A301967 A208640

Adjacent sequences: A120042 A120043 A120044 * A120046 A120047 A120048

Keyword

nonn,hard,more

Author

Robert G. Wilson v, Feb 15 2006

Extensions

a(12) from Chai Wah Wu, Jun 05 2026

a(13) from Chai Wah Wu, Jun 22 2026

Status

approved