|
| |
|
|
A173190
|
|
Values of n such that tau(n) = rad(n)^2, where tau(n) is the number of divisor of n, and rad(n) is the product of the distinct prime factors of n (rad(1)=1).
|
|
0
|
|
|
|
1, 8, 6561, 6912, 7776, 18432, 52488, 393216, 708588, 258280326, 327680000, 1000000000, 2097152000, 1007769600000, 1612431360000, 1813985280000, 2149908480000, 3936600000000, 6122200320000, 6561000000000, 7652750400000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
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. 840.
B. Spearman and K. S. Williams, Handbook of Estimates in the Theory of Numbers, Carleton Math. Lecture Note Series No. 14, 1975; see p. 2.1. E. C. Titchmarsh, The Theory of Functions, Oxford, 1938, p. 160.
|
|
|
LINKS
|
Table of n, a(n) for n=1..21.
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].
C. K. Caldwell, The Prime Glossa, Number of divisors
J. J. Holt & J. W. Jones, Discovering Number Theory, Section 1.4, Counting Divisors
|
|
|
EXAMPLE
|
tau(1) = 1, rad(1) = 1, and tau(1) = rad(1)^2 tau(8) = 4, rad(8) = 2, and tau(8) = rad(8)^2 tau(6561) = 9, rad(6561) = 3, and tau(6561) = rad(6561)^2
|
|
|
MAPLE
|
with(numtheory): for n from 1 to 50000000 do : t1 := ifactors(n)[2] : t2 := mul(t1[i][1], i=1..nops(t1)): if tau(n) = t2*t2 then print (n): else fi : od :
|
|
|
CROSSREFS
|
Sequence in context: A079189 A114133 A221233 * A115442 A216936 A090494
Adjacent sequences: A173187 A173188 A173189 * A173191 A173192 A173193
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Michel Lagneau, Feb 12 2010
|
|
|
EXTENSIONS
|
a(10)-a(21) from Donovan Johnson, Feb 13 2010
|
|
|
STATUS
|
approved
|
| |
|
|
