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A080681 17-smooth numbers: numbers whose prime divisors are all <= 17. 13
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 49, 50, 51, 52, 54, 55, 56, 60, 63, 64, 65, 66, 68, 70, 72, 75, 77, 78, 80, 81, 84, 85, 88, 90, 91, 96, 98, 99, 100, 102, 104, 105 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

William A. Tedeschi, Table of n, a(n) for n = 1..10000

FORMULA

Sum_{n>=1} 1/a(n) = Product_{primes p <= 17} p/(p-1) = (2*3*5*7*11*13*17)/(1*2*4*6*10*12*16) = 17017/3072. - Amiram Eldar, Sep 22 2020

MATHEMATICA

mx = 120; Sort@ Flatten@ Table[ 2^i*3^j*5^k*7^l*11^m*13^n*17^o, {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)]}, {n, 0, Log[13, mx/(2^i*3^j*5^k*7^l*11^m)]}, {o, 0, Log[17, mx/(2^i*3^j*5^k*7^l*11^m*13^n)]}] (* Robert G. Wilson v, Aug 17 2012 *)

PROG

(PARI) test(n)= {m=n; forprime(p=2, 17, while(m%p==0, m=m/p)); return(m==1)}

for(n=1, 200, if(test(n), print1(n", ")))

(PARI) list(lim, p=17)=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(17)]; // Bruno Berselli, Sep 24 2012

(Python)

import heapq

from itertools import islice

from sympy import primerange

def agen(p=17): # 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(), 70))) # Michael S. Branicky, Nov 20 2022

CROSSREFS

For p-smooth numbers with other values of p, see A003586, A051037, A002473, A051038, A080197, A080682, A080683.

Sequence in context: A076121 A239427 A255422 * A272322 A356800 A246079

Adjacent sequences: A080678 A080679 A080680 * A080682 A080683 A080684

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, Mar 02 2003

STATUS

approved

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Last modified December 6 21:00 EST 2022. Contains 358648 sequences. (Running on oeis4.)