A291880 Numbers n such that phi(n) - 1 | sigma(n).

3, 4, 5, 6, 8, 10, 20, 22, 40, 76, 80, 108, 160, 204, 320, 640, 1072, 1280, 2560, 4192, 5120, 10240, 20480, 40960, 49344, 81920, 163840, 327680, 655360, 1310720, 2621440, 4197376, 5242880, 10485760, 20971520, 41943040, 83886080, 167772160, 268460032, 335544320, 671088640, 1073790976, 1342177280, 2684354560, 5368709120

Offset: 1

Author

Paolo P. Lava, Sep 05 2017

Keywords

• nonn

Comments

Numbers n such that A109606(n) | A000203(n).

All numbers of the form 5*2^x, with x >= 0, are part of the sequence (A020714).

Values of the ratio sigma(n)/(phi(n)-1) are 4, 7, 2, 12, 5, 6, 6, 4, 6, 4, 6, 8, 6, 8, 6, 6, 4, 6, 6, 4, 6, 6, 6, 6, 8, 6, 6, 6, 6, 6, 6, 4, 6, ...

Sequence contains also terms of the form 2^(n-2)*(2^n+3) where 2^n+3 is a prime and n > 3, like 22, 76, 1072, 4192, 4197376, 268460032. See A057733 for primes of the form 2^n+3. - Michel Marcus, Sep 17 2017

Examples

			sigma(1072) = 2108, phi(1072) = 528 and 2108/(528 - 1) = 4.
		

Crossrefs

Cf. A000010, A000203, A020714, A056097, A057733, A109606.

Programs

Maple

with(numtheory): P:=proc(q) local n; for n from 3 to q do
if type(sigma(n)/(phi(n)-1),integer) then  print(n); fi; od;  end: P(10^7);

Mathematica

Select[Range[3, 10^6], Divisible[DivisorSigma[1, #], EulerPhi[#] - 1] &] (* Michael De Vlieger, Sep 06 2017 *)

PARI

isok(n) = denominator(sigma(n)/(eulerphi(n)-1)) == 1; \\ Michel Marcus, Sep 06 2017

Extensions

a(34)-a(41) from Michel Marcus, Sep 15 2017

a(42)-a(45) from Michel Marcus, Sep 21 2017