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%I #22 Nov 09 2020 06:25:40
%S 1,96,864,1080,1782,6144,7128,7776,17280,27000,28512,54432,55296,
%T 69984,87480,114048,215622,276480,381024,393216,432000,433026,456192,
%U 497664,629856,675000,862488,1382400,1399680,1677312,1732104,1824768,2187000,2195424,2667168
%N Numbers n such that rad(n)^2 divides sigma(n).
%C rad(n) is the product of the primes dividing n (A007947) and sigma(n) = sum of divisors of n (A000203). Considering the integers n = (2^a)*(3^b), where a+1 = 6k and b >= 1, we obtain an infinite number of numbers such that rad(n)^2 divides sigma(n).
%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.
%H Donovan Johnson, <a href="/A173615/b173615.txt">Table of n, a(n) for n = 1..300</a>
%H K. Broughan, J.-M. De Koninck, I. Kátai, and F. Luca, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Broughan/broughan20.html">On integers for which the sum of divisors is the square of the squarefree core</a>, J. Integer Seq., 15 (2012), pp. 1-12. See Final remarks pp. 10-11.
%H W. Sierpinski, <a href="http://matwbn.icm.edu.pl/ksiazki/mon/mon42/mon4204.pdf">Number Of Divisors And Their Sum</a>, Elementary theory of numbers, Warszawa, 1964.
%e rad(96)^2 = 6^2 = 36, sigma(96) = 252 and 36 divides 252
%p for n from 1 to 2000000 do : t1:= ifactors(n)[2] : t2 :=mul(t1[i][1], i=1..nops(t1)): if irem(sigma(n),t2^2) = 0 then print (n): else fi: od :
%o (PARI) isok(n) = my(f=factor(n)); (sigma(f) % factorback(f[, 1])^2) == 0; \\ _Michel Marcus_, Nov 09 2020
%Y Cf. A000203, A007947.
%K nonn
%O 1,2
%A _Michel Lagneau_, Feb 22 2010
%E a(30)-a(35) from _Donovan Johnson_, Jan 14 2012
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