login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 * A289441 A291272 A291273

Adjacent sequences:  A212172 A212173 A212174 * A212176 A212177 A212178

KEYWORD

nonn,tabf

AUTHOR

Matthew Vandermast, Jun 03 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 21 07:01 EST 2017. Contains 294989 sequences.