S000719


Least prime p such that phi(f(p)) < f(p)/n, where phi is Euler’s totient function and f(p) is the product of the primes up to p.

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, 195199273, 342243401, 600036917

2

S000719

The 30th term (20657677) produces a number almost 9000000 digits long!

T. D. Noe, Plot of 35 terms

Wikipedia, Euler’s totient function

(Mma) pr = 1; i = 0; Table[While[i++; pr = pr*Prime[i]/(Prime[i] - 1); pr < n]; Prime[i], {n, 2, 20}]

Cf. A091456 (primorials of the first of these numbers).

nonn,hard

T. D. Noe, Oct 12 2015

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