|
|
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
|
|
|
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
|
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].
|
|
FORMULA
|
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
|
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|