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A364549
Odd numbers k that divide A005941(k).
4
1, 3, 5, 97, 345, 549, 1093, 64621, 671515, 3280317, 8957089
OFFSET
1,2
COMMENTS
Sequence A005940(A364547(.)) sorted into ascending order.
Odd numbers k such that k divides 1+A156552(k).
The first ten terms factored:
1 (unity)
3 (prime)
5 (prime)
97 (prime)
345 = 3*5*23
549 = 3^2 * 61
1093 (prime)
64621 (prime)
671515 = 5*13*10331
3280317 = 3*79*13841.
Primes p present are those that occur as factors of 1 + 2^(A000720(p)-1).
PROG
(PARI)
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)
isA364549(n) = ((n%2)&&!(A005941(n)%n));
(Python)
from itertools import count, islice
from sympy import primepi, factorint
def A364549_gen(startvalue=1): # generator of terms >= startvalue
for n in count(max(startvalue+(startvalue&1^1), 1), 2):
if not (sum(pow(2, i+int(primepi(p))-1, n) for i, p in enumerate(factorint(n, multiple=True)))+1) % n:
yield n
A364549_list = list(islice(A364549_gen(), 8)) # Chai Wah Wu, Jul 28 2023
CROSSREFS
Odd terms in A364548.
Cf. also A364498, A364547, A364551.
Sequence in context: A056244 A173487 A279310 * A103081 A338269 A371194
KEYWORD
nonn,more
AUTHOR
Antti Karttunen, Jul 28 2023
EXTENSIONS
a(11) from Chai Wah Wu, Jul 28 2023
STATUS
approved