login
A307843
Divisors of Fermat numbers.
5
1, 3, 5, 17, 257, 641, 65537, 114689, 274177, 319489, 974849, 2424833, 6700417, 13631489, 26017793, 45592577, 63766529, 167772161, 825753601, 1214251009, 4294967297, 6487031809, 70525124609, 190274191361, 311453532161, 646730219521, 2710954639361
OFFSET
1,2
COMMENTS
Has both A000215 and A023394 as subsequences. Outside these are 1 and the composite proper divisors of Fermat numbers, namely 311453532161, 2983954661377, 7313319444481, ...
Odd m = (p_1)^(e_1)*(p_2)^(e_2)*...*(p_r)^(e_r) is a term if and only if the multiplicative order of 2 modulo (p_i)^(e_i) is the same power of 2 for 1 <= i <= r. - Jianing Song, May 19 2024
LINKS
Jeppe Stig Nielsen, Table of n, a(n) for n = 1..58
EXAMPLE
311453532161 is included because it divides 2^(2^11) + 1. It is not included in A023394 because it is composite.
PROG
(PARI) isA307843(n) = if(n==1, return(1)); if(n%2, my(f = factor(n), d = znorder(Mod(2, f[1, 1]^f[1, 2]))); if(!isprimepower(2*d), return(0)); for(i=2, #f~, if(znorder(Mod(2, f[i, 1]^f[i, 2])) != d, return(0))); 1, 0) \\ Jianing Song, May 19 2024. Inefficient to print the sequence as terms are sparse
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeppe Stig Nielsen, Jul 24 2019
STATUS
approved