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Numbers k such that for every prime divisor p of k, p-1 divides k-1.
6

%I #10 Apr 23 2021 05:10:51

%S 1,2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,31,32,37,41,43,45,47,49,

%T 53,59,61,64,67,71,73,79,81,83,89,97,101,103,107,109,113,121,125,127,

%U 128,131,137,139,149,151,157,163,167,169,173,179,181,191,193,197,199,211

%N Numbers k such that for every prime divisor p of k, p-1 divides k-1.

%C This sequence contains all powers of prime numbers (A000961). The remaining numbers form the sequence A087442.

%H Amiram Eldar, <a href="/A087441/b087441.txt">Table of n, a(n) for n = 1..10000</a>

%e 45 is in A087441 because its prime divisors are 3 and 5 and 3-1 = 2 as well as 5-1 = 4 divide 45-1 = 44.

%t Join[{1},Select[Range[2,300],And@@Divisible[#-1,FactorInteger[#][[All, 1]]-1]&]] (* _Harvey P. Dale_, Aug 07 2019 *)

%o (GAP) for i in [1..225] do if i = 1 or IsSubset (DivisorsInt(i-1), Set (FactorsInt (i)) - 1) then Print (i, ", "); fi; od;

%Y Cf. A000961, A087442.

%K easy,nonn

%O 1,2

%A _Jens Voß_, Sep 04 2003