A351563 a(n) is the exponent of the second smallest prime factor of n, or 0 if n is a power of a prime.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Apr 01 2022

Keywords

• nonn

Examples

			For n = 4 = 2^2 there is no second smallest prime factor as 4 is a power of prime, therefore a(4) = 0.
For n = 18 = 2^1 * 3^2, the exponent of the second smallest prime factor (3) is 2, therefore a(18) = 2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

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

Cf. also A119288, A351567.

Programs

Mathematica

Array[If[Length[#] < 2, 0, #[[2, -1]]] &@ FactorInteger[#] &, 108] (* Michael De Vlieger, Apr 01 2022 *)

PARI

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

Formula

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