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

1,1

Comments

A000244 is a subset of this sequence.

Links

Giovanni Resta, Table of n, a(n) for n = 1..73 (terms < 2*10^12)

Formula

Solutions of the equation A024816(n) mod A000203(n) = A000010(n).

Example

27*28/2 mod sigma(27) = 378 mod 40 = 18 = phi(27).

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);

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 *)

Crossrefs

Cf. A000010, A000203, A000244, A024816, A232324, A272337.

Sequence in context: A181140 A291007 A038002 * A249019 A216096 A300148

Adjacent sequences: A272335 A272336 A272337 * A272339 A272340 A272341

Keyword

nonn,easy

Author

Paolo P. Lava, Apr 26 2016

Extensions

a(27)-a(34) from Giovanni Resta, May 01 2016

Status

approved