OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is 1/2 (Bateman et al., 1981). - Amiram Eldar, Apr 25 2024
REFERENCES
József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter III, p. 119, section III.51.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Paul T. Bateman, Paul Erdős, Carl Pomerance and E. G. Straus, The arithmetic mean of the divisors of an integer, in Marvin I. Knopp (ed.), Analytic Number Theory, Proceedings of a Conference Held at Temple University, Philadelphia, May 12-15, 1980, Lecture Notes in Mathematics, Vol. 899, Springer, Berlin - New York, 1981, pp. 197-220, alternative link.
MAPLE
with(numtheory): t := [ ]: f := [ ]: for n from 1 to 500 do if sigma(n) mod sigma[ 0 ](n)^2 = 0 then t := [ op(t), n ] else f := [ op(f), n ]; fi; od: f;
MATHEMATICA
Select[Range[1, 100], !Divisible[DivisorSigma[1, #], DivisorSigma[0, #]^2] &] (* Amiram Eldar, Apr 25 2024 *)
PROG
(PARI) is(n) = {my(f = factor(n)); sigma(f) % numdiv(f)^2 > 0; } \\ Amiram Eldar, Apr 25 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved