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A051038 11-smooth numbers: numbers whose prime divisors are all <= 11. 37
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72, 75, 77, 80, 81, 84, 88, 90, 96, 98, 99, 100, 105, 108, 110, 112, 120, 121, 125, 126, 128, 132, 135, 140 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A155182 is a finite subsequence. - Reinhard Zumkeller, Jan 21 2009

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 *)

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

CROSSREFS

Subsequence of A033620.

For p-smooth numbers with other values of p, see A003586, A051037, A002473, A080197, A080681, A080682, A080683.

Sequence in context: A033637 A084034 A084347 * A140332 A155182 A096076

Adjacent sequences:  A051035 A051036 A051037 * A051039 A051040 A051041

KEYWORD

easy,nonn

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified November 25 06:17 EST 2020. Contains 338617 sequences. (Running on oeis4.)