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A361075
Products of exactly 7 distinct odd primes.
1
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
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
KEYWORD
nonn
AUTHOR
Karl-Heinz Hofmann, Mar 01 2023
STATUS
approved