

A212175


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.


2



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, 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, 2, 2, 7, 11, 4, 3, 8, 2, 0, 3, 2, 5, 4, 6, 2, 10, 5, 7, 3
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OFFSET

1,3


COMMENTS

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


LINKS

Table of n, a(n) for n=1..87.
Will Nicholes, Prime Signatures


FORMULA

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


EXAMPLE

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}.


CROSSREFS

Cf. A025487, A212172, A212176, A212178.
A124832 gives all positive exponents in prime factorization of A025487(n) for n > 1.
Sequence in context: A092915 A063749 A231333 * A289441 A291272 A291273
Adjacent sequences: A212172 A212173 A212174 * A212176 A212177 A212178


KEYWORD

nonn,tabf


AUTHOR

Matthew Vandermast, Jun 03 2012


STATUS

approved



