A329616 - OEIS

%I #13 Nov 18 2019 16:42:42

%S 0,1,1,2,1,3,1,3,2,3,1,3,1,3,3,4,1,3,1,3,3,3,1,5,2,3,3,3,1,3,1,5,3,3,

%T 3,6,1,3,3,5,1,3,1,3,3,3,1,5,2,3,3,3,1,7,3,5,3,3,1,7,1,3,3,6,3,3,1,3,

%U 3,3,1,7,1,3,3,3,3,3,1,5,4,3,1,7,3,3,3,5,1,7,3,3,3,3,3,7,1,3,3,6,1,3,1,5,3

%N Bitwise-OR of exponents of prime factors of A108951(n), where A108951 is fully multiplicative with a(prime(i)) = prime(i)# = Product_{i=1..i} A000040(i).

%C Positions of records are: 1, 2, 4, 6, 16, 24, 36, 54, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 65536, ..., conjectured also to be the positions of the first occurrence of each n.

%H Antti Karttunen, <a href="/A329616/b329616.txt">Table of n, a(n) for n = 1..65537</a>

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

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%F a(n) = A267116(A108951(n)) = A267116(A329600(n)).

%F a(n) >= A007814(n).

%F a(n) >= A329615(n).

%F a(n) >= A329647(n).

%o (PARI)

%o A034386(n) = prod(i=1, primepi(n), prime(i));

%o A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951

%o A267116(n) = if(n>1, fold(bitor, factor(n)[, 2]), 0); \\ From A267116

%o A329616(n) = A267116(A108951(n));

%Y Cf. A007814, A034386, A108951, A267116, A329600, A329615, A329647.

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 17 2019