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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
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: A278384 A114133 A221233 * A291879 A281450 A354564
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 12 2010
EXTENSIONS
a(10)-a(21) from Donovan Johnson, Feb 13 2010
STATUS
approved

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Last modified February 29 07:23 EST 2024. Contains 370414 sequences. (Running on oeis4.)