

A091440


Smallest number m such that m#/phi(m#) >= n, where m# indicates the primorial (A034386) of m and phi is Euler's totient function.


2



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
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OFFSET

1,2


COMMENTS

Does the ratio of adjacent terms converge?
For n > 1, a(n) is smallest prime p = prime(k) such that not less than (n1)/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


LINKS

Table of n, a(n) for n=1..34.
Eric Weisstein's World of Mathematics, Totient Function
Eric Weisstein's World of Mathematics, Primorial


EXAMPLE

7#/phi(7#) = (2*3*5*7)/(1*2*4*6) = 4.375 >= 4, 5#/phi(5#) = 3.75. Hence a(4) = 7.


MATHEMATICA

prod=1; i=0; Table[While[prod<n, i++; prod=prod/(11/Prime[i])]; Prime[i], {n, 1, 20}]


PROG

(PARI) al(lim) = local(mm, n, m); mm=3; n=2; m=1; forprime(x=3, lim, n*=x; m*= (x1); 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. AdamsWatters, Aug 29 2009


CROSSREFS

Cf. A091439, A000010, A002110, A034386, A053144, A038110, A060753, A164347.
Sequence in context: A144104 A088175 A271827 * A175211 A075058 A213968
Adjacent sequences: A091437 A091438 A091439 * A091441 A091442 A091443


KEYWORD

nonn


AUTHOR

T. D. Noe, Jan 09 2004


EXTENSIONS

More terms from David W. Wilson, Sep 28 2005
Sequence reference in name corrected by Peter Munn, Apr 29 2017


STATUS

approved



