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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 A278854 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

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Last modified September 22 12:52 EDT 2019. Contains 327307 sequences. (Running on oeis4.)