A087441 Numbers k such that for every prime divisor p of k, p-1 divides k-1.

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, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211

Offset: 1

Author

Jens Voß, Sep 04 2003

Keywords

• easy
• nonn

Comments

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000961, A087442.

Programs

GAP

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

Mathematica

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