OFFSET
1,1
COMMENTS
Numbers of the form 2^r*3^s*5^t*7^u*11^v with r, s, t, u >= 0, v > 0.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = 11 * A051038(n). - David A. Corneth, May 27 2017
Sum_{n>=1} 1/a(n) = 7/16. - Amiram Eldar, Nov 10 2020
EXAMPLE
33 = 3*11 is a term but 35 = 5*7 is not.
MAPLE
N:= 10^6; # to get all terms <= N
A:= NULL;
for v from 1 to floor(log[11](N)) do
V:= 11^v;
for u from 0 to floor(log[7](N/V)) do
U:= 7^u*V;
for t from 0 to floor(log[5](N/U)) do
T:= 5^t*U;
for s from 0 to floor(log[3](N/T)) do
S:= 3^s*T;
for r from 0 to floor(log[2](N/S)) do
A:= A, 2^r*S
od
od
od
od
od:
{A}; # Robert Israel, May 28 2014
MATHEMATICA
Select[Range[1000], FactorInteger[#][[-1, 1]] == 11 &] (* Amiram Eldar, Nov 10 2020 *)
PROG
(PARI) {m=1100; z=[]; for(r=0, floor(log(m)/log(2)), a=2^r; for(s=0, floor(log(m/a)/log(3)), b=a*3^s; for(t=0, floor(log(m/b)/log(5)), c=b*5^t; for(u=0, floor(log(m/c)/log(7)), d=c*7^u; for(v=1, floor(log(m/d)/log(11)), z=concat(z, d*11^v)))))); z=vecsort(z); for(i=1, length(z), print1(z[i], ", "))}
(Python)
from sympy import integer_log, prevprime
def A080195(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 11*bisection(f, n, n) # Chai Wah Wu, Oct 22 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Klaus Brockhaus, Feb 10 2003
STATUS
approved