

A236375


Positive integers m with 2^(m1)*phi(m)  1 prime, where phi(.) is Euler's totient function.


2



3, 7, 12, 15, 18, 31, 42, 108, 124, 140, 143, 155, 207, 327, 386, 463, 514, 823, 925, 1035, 1393, 1425, 2425, 3873, 5091, 5314, 5946, 12813, 14198, 15823, 19932, 22747, 37989, 38772
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OFFSET

1,1


COMMENTS

According to the conjecture in A236374, this sequence should have infinitely many terms.
The prime 2^(a(34)1)*phi(a(34))  1 = 2^(38771)*12888  1 has 11676 decimal digits.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..34


EXAMPLE

a(1) = 3 since neither 2^(11)*phi(1)  1 = 0 nor 2^(21)*phi(2)  1 = 1 is prime, but 2^(31)*phi(3)  1 = 4*2  1 = 7 is prime.


MATHEMATICA

q[m_]:=PrimeQ[2^(m1)*EulerPhi[m]1]
n=0; Do[If[q[m], n=n+1; Print[n, " ", m]], {m, 1, 10000}]


PROG

(PARI) s=[]; for(m=1, 1000, if(isprime(2^(m1)*eulerphi(m)1), s=concat(s, m))); s \\ Colin Barker, Jan 24 2014


CROSSREFS

Cf. A000010, A000040, A000079, A236374.
Sequence in context: A310225 A310226 A062731 * A310227 A310228 A310229
Adjacent sequences: A236372 A236373 A236374 * A236376 A236377 A236378


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Jan 24 2014


STATUS

approved



