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A147572
Numbers with exactly 5 distinct prime divisors {2,3,5,7,11}.
9
2310, 4620, 6930, 9240, 11550, 13860, 16170, 18480, 20790, 23100, 25410, 27720, 32340, 34650, 36960, 41580, 46200, 48510, 50820, 55440, 57750, 62370, 64680, 69300, 73920, 76230, 80850, 83160, 92400, 97020, 101640, 103950, 110880, 113190, 115500, 124740, 127050
OFFSET
1,1
COMMENTS
Successive numbers k such that EulerPhi(x)/x = m:
( Family of sequences for successive n primes )
m=1/2 numbers with exactly 1 distinct prime divisor {2} see A000079
m=1/3 numbers with exactly 2 distinct prime divisors {2,3} see A033845
m=4/15 numbers with exactly 3 distinct prime divisors {2,3,5} see A143207
m=8/35 numbers with exactly 4 distinct prime divisors {2,3,5,7} see A147571
m=16/77 numbers with exactly 5 distinct prime divisors {2,3,5,7,11} see A147572
m=192/1001 numbers with exactly 6 distinct prime divisors {2,3,5,7,11,13} see A147573
m=3072/17017 numbers with exactly 7 distinct prime divisors {2,3,5,7,11,13,17} see A147574
m=55296/323323 numbers with exactly 8 distinct prime divisors {2,3,5,7,11,13,17,19} see A147575
LINKS
FORMULA
a(n) = 2310 * A051038(n). - Amiram Eldar, Mar 10 2020
Sum_{n>=1} 1/a(n) = 1/480. - Amiram Eldar, Nov 12 2020
MATHEMATICA
a = {}; Do[If[EulerPhi[x]/x == 16/77, AppendTo[a, x]], {x, 1, 100000}]; a
Select[Range[130000], FactorInteger[#][[All, 1]]=={2, 3, 5, 7, 11}&] (* Harvey P. Dale, Oct 04 2020 *)
PROG
(Python)
from sympy import integer_log, prevprime
def A147572(n):
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
def g(x, m): return sum((x//3**i).bit_length() for i in range(integer_log(x, 3)[0]+1)) if m==3 else sum(g(x//(m**i), prevprime(m))for i in range(integer_log(x, m)[0]+1))
def f(x): return n+x-g(x, 11)
return 2310*bisection(f, n, n) # Chai Wah Wu, Sep 16 2024
KEYWORD
nonn
AUTHOR
Artur Jasinski, Nov 07 2008
EXTENSIONS
More terms from Amiram Eldar, Mar 10 2020
STATUS
approved