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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 (list; graph; refs; listen; history; text; internal format)
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 (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

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/(1-1/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*= (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

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

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Last modified May 29 01:07 EDT 2017. Contains 287241 sequences.