A340093 Composite numbers k such that A003958(k) divides k-1.

4, 8, 9, 16, 32, 64, 81, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 180225, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648

Offset: 1

Author

Antti Karttunen, Dec 31 2020

Keywords

• nonn
• more

Comments

Composite numbers k for which A340082(k) = 1.

Are there any other non-powers of 2 apart from 9, 81, 180225 (= 3^4 * 5^2 * 89) present?

If there are no squarefree numbers in this sequence, then Lehmer's Totient problem has no composite solutions.

Links

• Wikipedia, Lehmer's totient problem

Crossrefs

Cf. A003958, A005117, A340082.

Cf. A000079 (subsequence from its term a(2)=4 onward).

Cf. also A160595.

Programs

Mathematica

f[n_] := Times @@ (((fct = FactorInteger[n])[[;; , 1]] - 1)^fct[[;; , 2]]); Select[Range[10^7], CompositeQ[#] && Divisible[# - 1, f[#]] &] (* Amiram Eldar, Dec 31 2020 *)

PARI

A003958(n) = if(1==n,n,my(f=factor(n)); for(i=1,#f~,f[i,1]--); factorback(f));
isA340093(n) = ((n>1)&&!isprime(n)&&!((n-1)%A003958(n)));

Extensions

More terms from Amiram Eldar, Dec 31 2020