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

Author

Matthew Vandermast, May 08 2014

Keywords

• nonn
• tabf

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).

Examples

			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.

Formula

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