A212175 - OEIS

%I #9 Jun 18 2012 13:11:01

%S 0,0,2,0,3,2,4,3,0,5,2,2,4,2,6,3,2,5,3,7,4,2,2,2,6,0,3,3,4,8,5,2,3,2,

%T 7,2,4,3,5,9,6,2,4,2,8,3,5,3,2,2,2,6,10,3,3,7,2,2,2,4,4,5,2,9,4,6,3,3,

%U 2,2,7,11,4,3,8,2,0,3,2,5,4,6,2,10,5,7,3

%N List of exponents >= 2 in canonical prime factorization of A025487(n) (first integer of each prime signature), in nonincreasing order, or 0 if no such exponent exists.

%C Length of row n equals A212178(n) if A212178(n) is positive, or 1 if A212178(n) = 0.

%C Row n of table represents second signature of A025487(n) (cf. A212172).  The use of 0 in the table to represent numbers with no exponents >=2 in their prime factorization accords with the usual OEIS practice of using 0 to represent nonexistent elements when possible. In comments, the second signature of squarefree numbers is represented as { }.

%H Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>

%F a(n) = A212172(A025487(n)).

%e 240 = 2^4*3*5 has 1 exponent in its canonical prime factorization that equals or exceeds 2 (namely, 4). Hence, 240's second signature is {4}. Since 240 = A025487(24), row 24 of the table represents the second signature {4}.

%Y Cf. A025487, A212172, A212176, A212178.

%Y A124832 gives all positive exponents in prime factorization of A025487(n) for n > 1.

%K nonn,tabf

%O 1,3

%A _Matthew Vandermast_, Jun 03 2012