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%I #6 Apr 03 2023 10:36:11
%S 1,8,6561,6912,7776,18432,52488,393216,708588,258280326,327680000,
%T 1000000000,2097152000,1007769600000,1612431360000,1813985280000,
%U 2149908480000,3936600000000,6122200320000,6561000000000,7652750400000
%N 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).
%D 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.
%D 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.
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H C. K. Caldwell, The Prime Glossa<a href="https://t5k.org/glossary/page.php?sort=Tau">, Number of divisors</a>
%H J. J. Holt & J. W. Jones, Discovering Number Theory, Section 1.4, <a href="http://www.math.mtu.edu/mathlab/COURSES/holt/dnt/divis4.html">Counting Divisors</a>
%e 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
%p 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 :
%K nonn
%O 1,2
%A _Michel Lagneau_, Feb 12 2010
%E a(10)-a(21) from _Donovan Johnson_, Feb 13 2010