A364497 - OEIS

%I #7 Jul 27 2023 08:17:54

%S 1,3,6,12,24,43,48,86,96,172,192,344,384,688,768,1177,1376,1536,2354,

%T 2752,3072,3503,4708,5504,6144,7006,9416,11008,12288,14012,18832,

%U 22016,24576,28024,37664,44032,49152,49477,56048,75328,88064,98304,98954,112096,150656,169413,176128,196608,197908,224192,301312,338826

%N Numbers k such that k divides A243071(k).

%C If n is present, then 2*n is also present, and vice versa.

%C A007283 is included as a subsequence, because it gives the known fixed points of map n -> A163511(n).

%C Sequence A163511(A364496(.)) sorted into ascending order.

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

%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 isA364497(n) = !(A243071(n)%n);

%Y Cf. A163511, A243071.

%Y Cf. A007283 (subsequence), A364498 (odd terms).

%Y Cf. also A364295, A364494, A364496.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 27 2023