A364498 Odd numbers k such that k divides A243071(k).

1, 3, 43, 1177, 3503, 49477, 169413, 428015, 4394113, 33228911

Offset: 1

Author

Antti Karttunen, Jul 27 2023

Keywords

• nonn
• more

Comments

Primes p present are those that occur as factors of (2^A000720(p))-1: 3, 43, 49477, 4394113, 33228911, ...

Examples

			1177 = 11 * 107, with A243071(1177) = 536870895 = 3*5*11*47*107*647, therefore 1177 is present. Note that 536870895 = 11111111111111111111111101111 in binary, with four 1-bits at the least significant end, followed by 0, and then 24 more 1-bits at the most significant end, so A163511(536870895) = A000040(1+4) * A000040(4+24) = 11 * 107.
		

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Odd terms in A364497.

Cf. A000720, A163511, A243071, A364256.

Programs

PARI

A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429
A156552(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]); res };
A243071(n) = if(n<=2, n-1, A054429(A156552(n)));
isA364498(n) = ((n%2)&&!(A243071(n)%n));

Extensions

a(10) from Chai Wah Wu, Jul 27 2023