The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 29 03:48 EDT 2024. Contains 372921 sequences. (Running on oeis4.)