OFFSET
1,2
COMMENTS
A155182 is a finite subsequence. - Reinhard Zumkeller, Jan 21 2009
From Federico Provvedi, Jul 09 2022: (Start)
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000 (First 5000 terms from Reinhard Zumkeller)
Eric Weisstein's World of Mathematics, Smooth Number.
FORMULA
Sum_{n>=1} 1/a(n) = Product_{primes p <= 11} p/(p-1) = (2*3*5*7*11)/(1*2*4*6*10) = 77/16. - Amiram Eldar, Sep 22 2020
MATHEMATICA
mx = 150; Sort@ Flatten@ Table[ 2^i*3^j*5^k*7^l*11^m, {i, 0, Log[2, mx]}, {j, 0, Log[3, mx/2^i]}, {k, 0, Log[5, mx/(2^i*3^j)]}, {l, 0, Log[7, mx/(2^i*3^j*5^k)]}, {m, 0, Log[11, mx/(2^i*3^j*5^k*7^l)]}] (* Robert G. Wilson v, Aug 17 2012 *)
aQ[n_]:=Max[First/@FactorInteger[n]]<=11; Select[Range[140], aQ[#]&] (* Jayanta Basu, Jun 05 2013 *)
Block[{k=5, primorial:=Times@@Prime@Range@#&}, Select[Range@200, #*EulerPhi@primorial@k==EulerPhi[#*primorial@k]&]] (* Federico Provvedi, Jul 09 2022 *)
PROG
(PARI) test(n)=m=n; forprime(p=2, 11, while(m%p==0, m=m/p)); return(m==1)
for(n=1, 200, if(test(n), print1(n", ")))
(PARI) list(lim, p=11)=if(p==2, return(powers(2, logint(lim\1, 2)))); my(v=[], q=precprime(p-1), t=1); for(e=0, logint(lim\=1, p), v=concat(v, list(lim\t, q)*t); t*=p); Set(v) \\ Charles R Greathouse IV, Apr 16 2020
(Magma) [n: n in [1..150] | PrimeDivisors(n) subset PrimesUpTo(11)]; // Bruno Berselli, Sep 24 2012
(Python)
import heapq
from itertools import islice
from sympy import primerange
def agen(p=11): # generate all p-smooth terms
v, oldv, h, psmooth_primes, = 1, 0, [1], list(primerange(1, p+1))
while True:
v = heapq.heappop(h)
if v != oldv:
yield v
oldv = v
for p in psmooth_primes:
heapq.heappush(h, v*p)
print(list(islice(agen(), 67))) # Michael S. Branicky, Nov 20 2022
(Python)
from sympy import integer_log, prevprime
def A051038(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 bisection(f, n, n) # Chai Wah Wu, Sep 16 2024
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
STATUS
approved