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Multiples of 3 which are members of A002473. Or multiples of 3 with the largest prime divisor < 10.
8

%I #27 Sep 23 2024 08:10:54

%S 3,6,9,12,15,18,21,24,27,30,36,42,45,48,54,60,63,72,75,81,84,90,96,

%T 105,108,120,126,135,144,147,150,162,168,180,189,192,210,216,225,240,

%U 243,252,270,288,294,300,315,324,336,360,375,378,384,405,420,432,441,450

%N Multiples of 3 which are members of A002473. Or multiples of 3 with the largest prime divisor < 10.

%H Michael S. Branicky, <a href="/A085126/b085126.txt">Table of n, a(n) for n = 1..10001</a> (first 1001 terms from Harvey P. Dale)

%F a(n) = 3*A002473(n). - _Chai Wah Wu_, Sep 18 2024

%F Sum_{n>=1} 1/a(n) = 35/24. - _Amiram Eldar_, Sep 23 2024

%t Select[3*Range[200],FactorInteger[#][[-1,1]]<10&] (* _Harvey P. Dale_, Apr 10 2019 *)

%o (Python)

%o from sympy import integer_log

%o def A085126(n):

%o def bisection(f,kmin=0,kmax=1):

%o while f(kmax) > kmax: kmax <<= 1

%o while kmax-kmin > 1:

%o kmid = kmax+kmin>>1

%o if f(kmid) <= kmid:

%o kmax = kmid

%o else:

%o kmin = kmid

%o return kmax

%o def f(x):

%o c = n+x

%o for i in range(integer_log(x,7)[0]+1):

%o for j in range(integer_log(m:=x//7**i,5)[0]+1):

%o for k in range(integer_log(r:=m//5**j,3)[0]+1):

%o c -= (r//3**k).bit_length()

%o return c

%o return bisection(f,n,n)*3 # _Chai Wah Wu_, Sep 17 2024

%o (Python) # faster for initial segment of sequence

%o import heapq

%o from itertools import islice

%o def A085126gen(): # generator of terms

%o v, oldv, h, psmooth_primes, = 1, 0, [1], [2, 3, 5, 7]

%o while True:

%o v = heapq.heappop(h)

%o if v != oldv:

%o yield 3*v

%o oldv = v

%o for p in psmooth_primes:

%o heapq.heappush(h, v*p)

%o print(list(islice(A085126gen(), 65))) # _Michael S. Branicky_, Sep 17 2024

%Y Intersection of A008585 and A002473.

%Y Cf. A085125, A085127, A085128, A085129, A080194, A085131, A085132.

%K easy,nonn

%O 1,1

%A _Amarnath Murthy_, Jul 06 2003

%E More terms from _David Wasserman_, Jan 28 2005

%E Offset changed to 1 by _Michael S. Branicky_, Sep 17 2024