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.

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

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: A231333 A357866 A331622 * A370595 A289441 A291272

Adjacent sequences: A212172 A212173 A212174 * A212176 A212177 A212178

Keyword

nonn,tabf

Author

Matthew Vandermast, Jun 03 2012

Status

approved