A361075 Products of exactly 7 distinct odd primes.

4849845, 5870865, 6561555, 7402395, 7912905, 8273265, 8580495, 8843835, 9444435, 10015005, 10140585, 10465455, 10555545, 10705695, 10818885, 10975965, 11565015, 11696685, 11996985, 12267255, 12777765, 12785955, 13096545, 13408395, 13498485, 13528515, 13667745, 13803405

Offset

1,1

Links

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Example

a(1)     =   4849845 = 3*5*7*11*13*17*19
a(9663)  = 253808555 = 5*7*11*13*17*19*157
a(9961)  = 258573315 = 3*5*7*11*13*17*1013
a(10000) = 259173915 = 3*5*7*11*13*41*421

Prog

(Python)
import numpy
from sympy import nextprime, sieve, primepi
k_upto = 14 * 10**6
array = numpy.zeros(k_upto, dtype="i4")
sieve_max_number = primepi(nextprime(k_upto // 255255))
for s in range(2, sieve_max_number):
    array[sieve[s]:k_upto][::sieve[s]] += 1
for s in range(2, sieve_max_number):
    array[sieve[s]**2:k_upto][::sieve[s]**2] = 0
print([k for k in range(1, k_upto, 2) if array[k] == 7])
(Python)
from math import prod, isqrt
from sympy import primerange, integer_nthroot, primepi
def A361075(n):
    def g(x, a, b, c, m): yield from (((d, ) for d in enumerate(primerange(b+1, isqrt(x//c)+1), a+1)) if m==2 else (((a2, b2), )+d for a2, b2 in enumerate(primerange(b+1, integer_nthroot(x//c, m)[0]+1), a+1) for d in g(x, a2, b2, c*b2, m-1)))
    def f(x): return int(n+x-sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x, 1, 2, 1, 7)))
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    return bisection(f, n, n) # Chai Wah Wu, Sep 10 2024

Crossrefs

Cf. A065091, A046388 (2 distinct odd primes).

Cf. A046389 (3 distinct odd primes), A046390 (4 distinct odd primes).

Cf. A046391 (5 distinct odd primes), A168352 (6 distinct odd primes).

Sequence in context: A034637 A043637 A232676 * A147580 A043662 A125834

Adjacent sequences: A361072 A361073 A361074 * A361076 A361077 A361078

Keyword

nonn

Author

Karl-Heinz Hofmann, Mar 01 2023

Status

approved