A212174 Row n of table represents second signature of A013929(n): list of exponents >= 2 in canonical prime factorization of A013929(n), in nonincreasing order.

2, 3, 2, 2, 4, 2, 2, 3, 2, 3, 2, 5, 2, 2, 3, 2, 2, 4, 2, 2, 2, 3, 3, 2, 2, 6, 2, 3, 2, 2, 2, 4, 4, 2, 3, 2, 2, 5, 2, 2, 2, 2, 3, 3, 2, 4, 2, 2, 3, 2, 2, 3, 2, 7, 2, 3, 3, 2, 4, 2, 2, 2, 2, 3, 2, 2, 5, 4, 2, 3, 2, 2, 2, 2, 4, 2, 2, 3, 2, 3, 6, 2, 2, 2, 3, 2, 2, 2

Offset: 1

Author

Matthew Vandermast, Jun 03 2012

Keywords

• nonn
• tabf

Comments

Length of row n equals A212177(n).

Examples

			First rows of table read: 2; 3; 2; 2; 4; 2; 2; 3;...
12 = 2^2*3 has positive exponents 2 and 1 in its prime factorization, but only exponents that are 2 or greater appear in a number's second signature. Hence, 12's second signature is {2}. Since 12 = A013929(4), row 4 of the table represents the second signature {2}.
		

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844.

Links

• Jason Kimberley, Table of i, a(i) for i = 1..4492 (n = 1..3917)
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• Primefan, The First 2500 Integers Factored (1st of 5 pages)

Crossrefs

Cf. A013929, A212172, A212175, A212176, A212177.

Programs

Magma

&cat[Reverse(Sort([pe[2]:pe in Factorisation(n)|pe[2]gt 1])):n in[1..247]]; // Jason Kimberley, Jun 13 2012

Formula

a(n) = A212172(A013929(n)).

This sequence is both the subsequence of A212171 formed by omitting all 1s and the subsequence of A212172 formed by omitting all 0's. - Jason Kimberley, Jun 13 2012