A364498 - OEIS

%I #16 Jul 27 2023 21:13:41

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

%N Odd numbers k such that k divides A243071(k).

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

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%e 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.

%o (PARI)

%o A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429

%o 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 };

%o A243071(n) = if(n<=2, n-1, A054429(A156552(n)));

%o isA364498(n) = ((n%2)&&!(A243071(n)%n));

%Y Odd terms in A364497.

%Y Cf. A000720, A163511, A243071, A364256.

%K nonn,more

%O 1,2

%A _Antti Karttunen_, Jul 27 2023

%E a(10) from _Chai Wah Wu_, Jul 27 2023