

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



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Length of row n equals A212177(n).


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)


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


EXAMPLE

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}.


PROG

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


CROSSREFS

Cf. A013929, A212172, A212175, A212176, A212177.
Sequence in context: A140087 A174329 A295312 * A160558 A241019 A023581
Adjacent sequences: A212171 A212172 A212173 * A212175 A212176 A212177


KEYWORD

nonn,tabf


AUTHOR

Matthew Vandermast, Jun 03 2012


STATUS

approved



