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A340093
Composite numbers k such that A003958(k) divides k-1.
0
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.
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. A000079 (subsequence from its term a(2)=4 onward).
Cf. also A160595.
Sequence in context: A375160 A285438 A089042 * A227243 A272575 A020145
KEYWORD
nonn,more
AUTHOR
Antti Karttunen, Dec 31 2020
EXTENSIONS
More terms from Amiram Eldar, Dec 31 2020
STATUS
approved