A212176 Row n of table lists exponents in canonical prime factorization of A181800(n) (n-th powerful number that is the first integer of its prime signature), in nonincreasing order.

2, 3, 4, 5, 2, 2, 6, 3, 2, 7, 4, 2, 3, 3, 8, 5, 2, 4, 3, 9, 6, 2, 5, 3, 2, 2, 2, 10, 7, 2, 4, 4, 6, 3, 3, 2, 2, 11, 8, 2, 5, 4, 7, 3, 4, 2, 2, 12, 9, 2, 6, 4, 3, 3, 2, 8, 3, 5, 2, 2, 5, 5, 13, 10, 2, 7, 4, 4, 3, 2, 9, 3, 6, 2, 2, 6, 5, 14, 11, 2, 8, 4, 5, 3, 2, 3

Offset

2,1

Comments

A212179(n) gives length of row n.

Table represents prime signature (cf. A212171) and second signature (cf. A212172) of A181800.

Links

Table of n, a(n) for n=2..87.

Will Nicholes, Prime Signatures

Formula

Row n is identical to row A181800(n) of tables A212171 and A212172.

Example

Since 72 is a member of A181800, all positive exponents in its prime factorization (2^3*3^2) equal or exceed 2. Therefore, its second signature is the same as its prime signature, namely, {3,2} (nonincreasing version).  Since 72 = A181800 (8), row 8 represents the prime signature and second signature {3,2}.

Crossrefs

Cf. A181800, A212171, A212172, A212179.

Sequence in context: A037839 A165072 A141404 * A070671 A119281 A328943

Adjacent sequences: A212173 A212174 A212175 * A212177 A212178 A212179

Keyword

nonn,tabf

Author

Matthew Vandermast, Jun 03 2012

Status

approved