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A091440
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Smallest number m such that m#/phi(m#) >= n, where m# indicates the primorial (A034386) of m and phi is Euler's totient function.
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5
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1, 2, 3, 7, 13, 23, 43, 79, 149, 257, 461, 821, 1451, 2549, 4483, 7879, 13859, 24247, 42683, 75037, 131707, 230773, 405401, 710569, 1246379, 2185021, 3831913, 6720059, 11781551, 20657677, 36221753, 63503639, 111333529, 195199289, 342243479, 600036989
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OFFSET
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1,2
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COMMENTS
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Does the ratio of adjacent terms converge?
It appears that lim_{n->infinity} a(n+1)/a(n) = 1.7532... - Jon E. Schoenfield, Feb 21 2019
For n > 1, a(n) is smallest prime p = prime(k) such that no fewer than (n-1)/n of any p# consecutive integers are divisible by a prime not greater than p. Cf. A053144(k)/A002110(k). - Peter Munn, Apr 29 2017
Also, the smallest prime p such that the sum of the reciprocals of the p-smooth numbers converges to at least n. - Keith F. Lynch, Apr 29 2023
Also, if m is a random integer much larger than the square of a(n), and m is not divisible by any prime less than or equal to a(n), the probability that m is prime is n/log(m). - Keith F. Lynch, Dec 17 2023
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LINKS
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Eric Weisstein's World of Mathematics, Primorial
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EXAMPLE
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7#/phi(7#) = (2*3*5*7)/(1*2*4*6) = 4.375 >= 4, 5#/phi(5#) = 3.75. Hence a(4) = 7.
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MATHEMATICA
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prod=1; i=0; Table[While[prod<n, i++; prod=prod/(1-1/Prime[i])]; Prime[i], {n, 1, 20}]
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PROG
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(PARI) al(lim) = local(mm, n, m); mm=3; n=2; m=1; forprime(x=3, lim, n*=x; m*= (x-1); if (n\m >= mm, print1(x", "); mm++)); /* This will generate all terms of this sequence from the 3rd onward, up to lim. The computation slows down for large values because of the size of the internal values. */ \\ Fred Schneider, Aug 13 2009, modified by Franklin T. Adams-Watters, Aug 29 2009
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Sequence reference in name corrected by Peter Munn, Apr 29 2017
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STATUS
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approved
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