A351563 - OEIS

%I #14 Apr 02 2022 10:26:11

%S 0,0,0,0,0,1,0,0,0,1,0,1,0,1,1,0,0,2,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,1,

%T 1,2,0,1,1,1,0,1,0,1,1,1,0,1,0,2,1,1,0,3,1,1,1,1,0,1,0,1,1,0,1,1,0,1,

%U 1,1,0,2,0,1,2,1,1,1,0,1,0,1,0,1,1,1,1,1,0,2,1,1,1,1,1,1,0,2,1,2,0,1,0,1,1,1,0,3

%N a(n) is the exponent of the second smallest prime factor of n, or 0 if n is a power of a prime.

%H Antti Karttunen, <a href="/A351563/b351563.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = A067029(A028234(n)).

%e For n = 4 = 2^2 there is no second smallest prime factor as 4 is a power of prime, therefore a(4) = 0.

%e For n = 18 = 2^1 * 3^2, the exponent of the second smallest prime factor (3) is 2, therefore a(18) = 2.

%t Array[If[Length[#] < 2, 0, #[[2, -1]]] &@ FactorInteger[#] &, 108] (* _Michael De Vlieger_, Apr 01 2022 *)

%o (PARI) A351563(n) = if(1>=omega(n), 0, (factor(n))[2,2]);

%Y Cf. A000961 (positions of zeros), A001221, A028234, A067029.

%Y Cf. also A119288, A351567.

%K nonn

%O 1,18

%A _Antti Karttunen_, Apr 01 2022