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%I #39 Dec 18 2023 12:22:23
%S 1,2,3,7,13,23,43,79,149,257,461,821,1451,2549,4483,7879,13859,24247,
%T 42683,75037,131707,230773,405401,710569,1246379,2185021,3831913,
%U 6720059,11781551,20657677,36221753,63503639,111333529,195199289,342243479,600036989
%N Smallest number m such that m#/phi(m#) >= n, where m# indicates the primorial (A034386) of m and phi is Euler's totient function.
%C Does the ratio of adjacent terms converge?
%C It appears that lim_{n->infinity} a(n+1)/a(n) = 1.7532... - _Jon E. Schoenfield_, Feb 21 2019
%C 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
%C 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
%C 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
%H Jon E. Schoenfield, <a href="/A091440/b091440.txt">Table of n, a(n) for n = 1..44</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Primorial.html">Primorial</a>
%e 7#/phi(7#) = (2*3*5*7)/(1*2*4*6) = 4.375 >= 4, 5#/phi(5#) = 3.75. Hence a(4) = 7.
%t prod=1; i=0; Table[While[prod<n, i++; prod=prod/(1-1/Prime[i])]; Prime[i], {n, 1, 20}]
%o (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
%Y Cf. A091439, A000010, A002110, A034386, A053144, A038110, A060753, A164347.
%K nonn
%O 1,2
%A _T. D. Noe_, Jan 09 2004
%E More terms from _David W. Wilson_, Sep 28 2005
%E Sequence reference in name corrected by _Peter Munn_, Apr 29 2017
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