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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 (list; graph; refs; listen; history; text; internal format)
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 * A008807 A263149 A008819

Adjacent sequences:  A212172 A212173 A212174 * A212176 A212177 A212178

KEYWORD

nonn,tabf

AUTHOR

Matthew Vandermast, Jun 03 2012

STATUS

approved

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Last modified March 25 21:19 EDT 2017. Contains 284111 sequences.