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

1,1

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

Table of n, a(n) for n=1..33.

Wikipedia, Lehmer's totient problem

Mathematica

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

Prog

(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)));

Crossrefs

Cf. A003958, A005117, A340082.

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

Cf. also A160595.

Sequence in context: A227645 A285438 A089042 * A227243 A272575 A020145

Adjacent sequences: A340090 A340091 A340092 * A340094 A340095 A340096

Keyword

nonn,more

Author

Antti Karttunen, Dec 31 2020

Extensions

More terms from Amiram Eldar, Dec 31 2020

Status

approved