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 A051038 11-smooth numbers: numbers whose prime divisors are all <= 11. 38
 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 From Federico Provvedi, Jul 09 2022: (Start) In general, if p=A000040(k) is the k-th prime, with k>1, p-smooth numbers are also those positive integers m such that A000010(A002110(k))*m == A000010(A002110(k)*m). With k=5, p = A000040(5) = 11, the primorial p# = A002110(5) = 2310, and its Euler totient is A000010(2310) = 480, so the 11-smooth numbers are also those positive integers m such that 480*m == A000010(2310*m). (End) 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 CROSSREFS Subsequence of A033620. For p-smooth numbers with other values of p, see A003586, A051037, A002473, A080197, A080681, A080682, A080683. A000010, A002110. 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 December 3 09:41 EST 2023. Contains 367539 sequences. (Running on oeis4.)