A155747 Smallest number m with property that 2^m-1 is divisible by first n odd primes.

2, 4, 12, 60, 60, 120, 360, 3960, 27720, 27720, 27720, 27720, 27720, 637560, 8288280, 240360120, 240360120, 240360120, 240360120, 240360120, 240360120, 9854764920, 9854764920, 19709529840, 98547649200, 1675310036400, 88791431929200

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..500

Formula

2^m == 1 (mod (primorial(n)/2)) == 1 (mod (A002110(n+1)/2)).

Example

n=1, m=2, 2^2-1=3;
n=2, m=4, 2^4-1=15=3*5;
n=3, m=12, 2^12-1=4095=(3*5*7)*39;
n=4, m=60, 2^60-1=1152921504606846975=(3*5*7*11)*998200436889045;
n=5, m=60, 2^60-1=1152921504606846975=(3*5*7*11*13)*76784648991465;
n=6, m=120, 2^120-1=1329227995784915872903807060280344575=(3*5*7*11*13*17)*5207451355644026063755096120665.

Mathematica

Table[LCM@@(MultiplicativeOrder[2, # ]& /@ Prime[Range[2, n]]), {n, 2, 50}] (* T. D. Noe, May 07 2010 *)

Prog

(PARI) a(n) = lcm(vector(n, k, znorder(Mod(2, prime(k+1))))); \\ Michel Marcus, Jun 25 2019

Crossrefs

Cf. A002110.

Sequence in context: A301481 A128648 A128646 * A058254 A076244 A058255

Adjacent sequences: A155744 A155745 A155746 * A155748 A155749 A155750

Keyword

nonn

Author

Zak Seidov, Jan 26 2009

Extensions

a(16)-a(21) from D. S. McNeil, Mar 04 2009

Extended by T. D. Noe, May 07 2010

Status

approved