A329378 - OEIS

%I #15 Nov 18 2019 16:41:50

%S 1,1,1,2,1,2,1,3,2,2,1,3,1,2,2,4,1,6,1,3,2,2,1,4,2,2,3,3,1,6,1,5,2,2,

%T 2,4,1,2,2,4,1,6,1,3,3,2,1,5,2,6,2,3,1,12,2,4,2,2,1,4,1,2,3,6,2,6,1,3,

%U 2,6,1,10,1,2,6,3,2,6,1,5,4,2,1,4,2,2,2,4,1,12,2,3,2,2,2,6,1,6,3,4,1,6,1,4,6

%N Least common multiple 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).

%H Antti Karttunen, <a href="/A329378/b329378.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</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) = A072411(A108951(n)) = A072411(A329600(n)).

%F a(n) <= A329617(n) <= A329382(n) <= A329605(n).

%F a(A019565(n)) = A284002(n).

%o (PARI)

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

%o A072411(n) = lcm(factor(n)[, 2]); \\ From A072411

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

%o A329378(n) = A072411(A108951(n));

%Y Cf. A019565, A034386, A072411, A108951, A284002, A329382, A329600, A329605.

%Y Differs from related A329617 for the first time at n=36.

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 17 2019