A143958 Integers n > 1 such that n-1 is divisible by the difference between the largest and smallest primes dividing n.

6, 10, 12, 15, 18, 21, 24, 33, 35, 36, 40, 45, 48, 54, 55, 56, 65, 72, 75, 77, 78, 85, 91, 96, 100, 105, 108, 126, 133, 135, 136, 143, 144, 145, 154, 160, 161, 162, 175, 187, 189, 192, 196, 209, 216, 217, 221, 225, 245, 247, 250, 253, 261, 288, 297, 323, 324, 336

Offset

1,1

Comments

If p is prime, (p+t)*p is in the sequence if t is a divisor of p^2-1 such that p+t is prime. - Robert Israel, Nov 27 2017

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The largest prime dividing 21 is 7. The smallest prime dividing 21 is 3. 7-3 = 4 divides 21-1 = 20. So 21 is in the sequence.

Maple

filter:= proc(n) local F;
  F:= [min, max](numtheory:-factorset(n));
  F[1]<F[2] and (n-1 mod (F[2]-F[1]) = 0)
end proc:
select(filter, [$2..1000]); # Robert Israel, Nov 27 2017

Mathematica

Select[Range[2, 336], Function[n, If[# == 0, False, Divisible[n - 1, #]] &[Last@ # - First@ #] &[FactorInteger[n][[All, 1]] ] ] ] (* Michael De Vlieger, Nov 27 2017 *)

Crossrefs

Cf. A143957.

Sequence in context: A324857 A279550 A362754 * A294278 A373677 A297366

Adjacent sequences: A143955 A143956 A143957 * A143959 A143960 A143961

Keyword

nonn

Author

Leroy Quet, Sep 05 2008

Extensions

Extended by Ray Chandler, Nov 07 2008

Name edited by Jon E. Schoenfield, Nov 27 2017

Status

approved