A124512 - OEIS

%I #18 Jul 11 2023 03:39:07

%S 1,144,144,288,144,576,144,576,288,576,144,1152,144,576,576,1152,144,

%T 1152,144,1152,576,576,144,2304,288,576,576,1152,144,2304,144,2304,

%U 576,576,576,2304,144,576,576,2304,144,2304,144,1152,1152,576,144,4608,288

%N a(n) = A124508(A124508(A124508(n))).

%H Antti Karttunen, <a href="/A124512/b124512.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A124508(A124511(n)) = A124511(A124508(n)).

%F a(n) = 4*A124511(n) for n > 1.

%F For primes p, q with p<>q: a(p) = 144; a(p*q) = 576; a(p^k) = 9*2^(k+3), k > 0.

%F a(n) = 9 * 2^(omega(n) + Omgea(n) + 2) = 9 * 2^(A001221(n) + A001222(n) + 2), for n >= 2. - _Amiram Eldar_, Jul 11 2023

%t a[n_] := 9 * 2^(PrimeNu[n] + PrimeOmega[n] + 2); a[1] = 1; Array[a, 100] (* _Amiram Eldar_, Jul 11 2023 *)

%o (PARI)

%o A124508(n) = (2^bigomega(n) * 3^omega(n));

%o A124512(n) = A124508(A124508(A124508(n))); \\ _Antti Karttunen_, Jul 07 2017

%o (PARI) a(n) = my(f = factor(n)); if(n == 1, 1, 9 * 2^(omega(f) + bigomega(f) + 2)); \\ _Amiram Eldar_, Jul 11 2023

%Y Cf. A001221, A001222, A003586, A124508, A124511.

%K nonn,easy

%O 1,2

%A _Reinhard Zumkeller_, Nov 04 2006