A366385 - OEIS

%I #16 Oct 23 2023 15:00:52

%S 0,1,2,2,3,4,4,4,6,6,5,8,6,8,9,8,7,12,8,12,12,10,9,16,15,12,18,16,10,

%T 18,11,16,15,14,20,24,12,16,18,24,13,24,14,20,27,18,15,32,28,30,21,24,

%U 16,36,25,32,24,20,17,36,18,22,36,32,30,30,19,28,27,40,20,48,21,24,45,32,35,36,22,48,54,26,23,48,35

%N Divide n by its largest prime factor, then multiply with the index of that same prime; a(1) = 0 by convention.

%H Antti Karttunen, <a href="/A366385/b366385.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Mat#matula">Index entries for sequences related to Matula-Goebel numbers</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>

%F a(n) = A052126(n)*A061395(n) = (n/A006530(n)) * A000720(A006530(n)).

%t Array[PrimePi[#2]*#1/#2 & @@ {#, FactorInteger[#][[-1, 1]]} &, 85] (* _Michael De Vlieger_, Oct 23 2023 *)

%o (PARI)

%o A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);

%o A366385(n) = { my(gpf=A006530(n)); primepi(gpf)*(n/gpf); };

%Y Cf. A000720, A006530, A052126, A061395.

%Y Cf. A196050 (number of iterations needed to reach 1), A366388 (number of iterations to reach the nearest power of 2), A109129 (exponent of the nearest power of 2 reached).

%Y Cf. also A366387, A324923.

%K nonn

%O 1,3

%A _Antti Karttunen_, Oct 23 2023