A272338 Numbers such that antisigma(n) mod sigma(n) = phi(n), where antisigma(n) is the sum of the numbers less than n that do not divide n, sigma(n) is the sum of the divisors of n and phi(n) is the Euler totient function of n.
3, 9, 27, 81, 243, 319, 729, 2187, 3615, 6561, 8159, 9807, 19683, 32791, 59049, 103679, 177147, 432864, 531441, 788852, 871215, 1594323, 2779519, 2826863, 2858240, 4782969, 7213536, 10036415, 14348907, 20428863, 24423359, 29036799, 33385279, 43046721
Offset: 1
Examples
27*28/2 mod sigma(27) = 378 mod 40 = 18 = phi(27).
Links
- Giovanni Resta, Table of n, a(n) for n = 1..73 (terms < 2*10^12)
Programs
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Maple
with(numtheory): P:=proc(q) local n; for n from 1 to q do if (n*(n+1)/2) mod sigma(n)=phi(n) then print(n); fi; od; end: P(10^6);
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Mathematica
Select[Range[10^5], Function[n, Mod[Total@ First@ #, Total@ Last@ #] == EulerPhi@ n &@ {Complement[Range@ n, #], #} &@ Divisors@ n]] (* Michael De Vlieger, Apr 27 2016 *)
Extensions
a(27)-a(34) from Giovanni Resta, May 01 2016
Comments