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A307843 Divisors of Fermat numbers.

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%I A307843 #28 May 19 2024 19:42:40
%S A307843 1,3,5,17,257,641,65537,114689,274177,319489,974849,2424833,6700417,
%T A307843 13631489,26017793,45592577,63766529,167772161,825753601,1214251009,
%U A307843 4294967297,6487031809,70525124609,190274191361,311453532161,646730219521,2710954639361
%N A307843 Divisors of Fermat numbers.
%C A307843 Has both A000215 and A023394 as subsequences. Outside these are 1 and the composite proper divisors of Fermat numbers, namely 311453532161, 2983954661377, 7313319444481, ...
%C A307843 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
%H A307843 Jeppe Stig Nielsen, <a href="/A307843/b307843.txt">Table of n, a(n) for n = 1..58</a>
%e A307843 311453532161 is included because it divides 2^(2^11) + 1. It is not included in A023394 because it is composite.
%o A307843 (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
%Y A307843 Cf. A000215, A023394, A050922, A094358.
%K A307843 nonn
%O A307843 1,2
%A A307843 _Jeppe Stig Nielsen_, Jul 24 2019