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

1,1

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

Links

Table of n, a(n) for n=1..45.

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A167057 A100585 A023367 * A047426 A362781 A323527

Adjacent sequences: A291877 A291878 A291879 * A291881 A291882 A291883

Keyword

nonn

Author

Paolo P. Lava, Sep 05 2017

Extensions

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

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

Status

approved