A049692 Numbers k such that the square of the number of divisors of k does not divide the sum of the divisors of k.
2, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20, 22, 24, 25, 26, 27, 28, 29, 30, 32, 34, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 60, 61, 63, 64, 65, 66, 68, 70, 72, 73, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86
Offset: 1
Keywords
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.
Programs
-
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 *)
-
PARI
is(n) = {my(f = factor(n)); sigma(f) % numdiv(f)^2 > 0;} \\ Amiram Eldar, Apr 25 2024
Comments