cp's OEIS Frontend

A364549 Odd numbers k that divide A005941(k).

%I A364549 #17 Jul 29 2023 01:21:07
%S A364549 1,3,5,97,345,549,1093,64621,671515,3280317,8957089
%N A364549 Odd numbers k that divide A005941(k).
%C A364549 Sequence A005940(A364547(.)) sorted into ascending order.
%C A364549 Odd numbers k such that k divides 1+A156552(k).
%C A364549 The first ten terms factored:
%C A364549         1   (unity)
%C A364549         3   (prime)
%C A364549         5   (prime)
%C A364549        97   (prime)
%C A364549       345 = 3*5*23
%C A364549       549 = 3^2 * 61
%C A364549      1093   (prime)
%C A364549     64621   (prime)
%C A364549    671515 = 5*13*10331
%C A364549   3280317 = 3*79*13841.
%C A364549 Primes p present are those that occur as factors of 1 + 2^(A000720(p)-1).
%o A364549 (PARI)
%o A364549 A005941(n) = { my(f=factor(n), p, p2=1, res=0); for(i=1, #f~, p = 1 << (primepi(f[i, 1])-1); res += (p * p2 * (2^(f[i, 2])-1)); p2 <<= f[i, 2]); (1+res) }; \\ (After _David A. Corneth_'s program for A156552)
%o A364549 isA364549(n) = ((n%2)&&!(A005941(n)%n));
%o A364549 (Python)
%o A364549 from itertools import count, islice
%o A364549 from sympy import primepi, factorint
%o A364549 def A364549_gen(startvalue=1): # generator of terms >= startvalue
%o A364549     for n in count(max(startvalue+(startvalue&1^1),1),2):
%o A364549         if not (sum(pow(2,i+int(primepi(p))-1,n) for i, p in enumerate(factorint(n, multiple=True)))+1) % n:
%o A364549             yield n
%o A364549 A364549_list = list(islice(A364549_gen(),8)) # _Chai Wah Wu_, Jul 28 2023
%Y A364549 Odd terms in A364548.
%Y A364549 Cf. A000720, A005940, A005941, A156552.
%Y A364549 Cf. also A364498, A364547, A364551.
%K A364549 nonn,more
%O A364549 1,2
%A A364549 _Antti Karttunen_, Jul 28 2023
%E A364549 a(11) from _Chai Wah Wu_, Jul 28 2023