A015715 Odd integers m such that phi(m) | sigma(m).

1, 3, 15, 35, 105, 357, 1045, 1485, 3135, 3339, 5049, 10659, 12441, 16065, 24871, 24969, 29029, 33915, 35343, 39105, 39585, 50065, 58435, 64285, 71145, 74613, 87087, 87685, 99693, 124355, 124605, 132957, 137885, 140335, 145145, 150195

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn

Comments

Subsequence of A236693. Proof: if n is in this sequence, then 2^phi(n) - 1 is divisible by n and 2^sigma(n) - 1 is divisible by 2^phi(n) - 1. Therefore, 2^sigma(n) == 1 (mod n) and n is in A236693. - Jinyuan Wang, Mar 13 2020

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Jud McCranie; terms 1..1000 from Donovan Johnson)

Crossrefs

Subsequence of A020492 and A236693.

Cf. A000010, A000203.

Programs

Mathematica

Select[Range[1,151001,2],Divisible[DivisorSigma[1,#],EulerPhi[#]]&] (* Harvey P. Dale, Sep 16 2016 *)

PARI

isok(m) = (m % 2) && !(sigma(m) % eulerphi(m)); \\ Michel Marcus, Mar 14 2020

Extensions

Offset corrected by Donovan Johnson, Jan 18 2012