The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A080682 19-smooth numbers: numbers whose prime divisors are all <= 19. 16
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 48, 49, 50, 51, 52, 54, 55, 56, 57, 60, 63, 64, 65, 66, 68, 70, 72, 75, 76, 77, 78, 80, 81, 84, 85, 88, 90, 91, 95, 96, 98, 99, 100 (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 <= 19} p/(p-1) = (2*3*5*7*11*13*17*19)/(1*2*4*6*10*12*16*18) = 323323/55296. - 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*19^p, {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)]}, {p, 0, Log[19, mx/(2^i*3^j*5^k*7^l*11^m*13^n*17^o)]}] (* Robert G. Wilson v, Jan 19 2016 *) Select[Range[100], Max[FactorInteger[#][[All, 1]]]<20&] (* Harvey P. Dale, Sep 20 2018 *) PROG (PARI) test(n)= {m=n; forprime(p=2, 19, while(m%p==0, m=m/p)); return(m==1)} for(n=1, 200, if(test(n), print1(n", "))) (PARI) list(lim, p=19)=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..100] | PrimeDivisors(n) subset PrimesUpTo(19)]; // Bruno Berselli, Sep 24 2012 (Python) import heapq from itertools import islice from sympy import primerange def agen(p=19): # 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(), 72))) # Michael S. Branicky, Nov 20 2022 CROSSREFS For p-smooth numbers with other values of p, see A003586, A051037, A002473, A051038, A080197, A080681, A080683. Sequence in context: A004830 A081330 A359415 * A182049 A038770 A342591 Adjacent sequences: A080679 A080680 A080681 * A080683 A080684 A080685 KEYWORD easy,nonn AUTHOR Cino Hilliard, Mar 02 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 29 10:23 EDT 2024. Contains 372936 sequences. (Running on oeis4.)