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A173615
Numbers n such that rad(n)^2 divides sigma(n).
2
1, 96, 864, 1080, 1782, 6144, 7128, 7776, 17280, 27000, 28512, 54432, 55296, 69984, 87480, 114048, 215622, 276480, 381024, 393216, 432000, 433026, 456192, 497664, 629856, 675000, 862488, 1382400, 1399680, 1677312, 1732104, 1824768, 2187000, 2195424, 2667168
OFFSET
1,2
COMMENTS
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).
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.
LINKS
K. Broughan, J.-M. De Koninck, I. Kátai, and F. Luca, On integers for which the sum of divisors is the square of the squarefree core, J. Integer Seq., 15 (2012), pp. 1-12. See Final remarks pp. 10-11.
W. Sierpinski, Number Of Divisors And Their Sum, Elementary theory of numbers, Warszawa, 1964.
EXAMPLE
rad(96)^2 = 6^2 = 36, sigma(96) = 252 and 36 divides 252
MAPLE
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 :
PROG
(PARI) isok(n) = my(f=factor(n)); (sigma(f) % factorback(f[, 1])^2) == 0; \\ Michel Marcus, Nov 09 2020
CROSSREFS
Sequence in context: A253410 A326576 A202890 * A103846 A203979 A296960
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 22 2010
EXTENSIONS
a(30)-a(35) from Donovan Johnson, Jan 14 2012
STATUS
approved