A238747 Row n of table gives prime metasignature of n: count total appearances of each distinct integer that appears in the prime signature of n, then arrange totals in nonincreasing order.

1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1, 1

Offset

2,5

Comments

A prime metasignature is analogous to the signature of a partition (cf. A115621); it is the signature of a prime signature.

Row n also gives prime signature of A181819(n).

Links

Table of n, a(n) for n=2..88.

Formula

Row n is identical to row A181819(n) of table A212171.

Example

The prime signature of 72 (2^3*3^2) is {3,2}. The numbers 3 and 2 each appear once; therefore, the prime metasignature of 72 is {1,1}.
The prime signature of 120 (2^3*3*5) is {3,1,1}. 3 appears 1 time and 1 appears 2 times; therefore, the prime metasignature of 120 is {2,1}.

Crossrefs

Length of row n equals A071625(n); sum of numbers in row n is A001221(n).

Cf. A115621, A181819, A238748.

Sequence in context: A143898 A332636 A353742 * A101873 A336691 A177991

Adjacent sequences: A238744 A238745 A238746 * A238748 A238749 A238750

Keyword

nonn,tabf

Author

Matthew Vandermast, May 08 2014

Status

approved