A364549 Odd numbers k that divide A005941(k).

1, 3, 5, 97, 345, 549, 1093, 64621, 671515, 3280317, 8957089

Offset: 1

Author

Antti Karttunen, Jul 28 2023

Keywords

• nonn
• more

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).

Crossrefs

Odd terms in A364548.

Cf. A000720, A005940, A005941, A156552.

Cf. also A364498, A364547, A364551.

Programs

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

Extensions

a(11) from Chai Wah Wu, Jul 28 2023