A086770 Numbers k such that the difference between the largest and the smallest prime divisor of k equals the number of prime divisors of k (counted with multiplicity).

1, 15, 20, 30, 35, 50, 112, 143, 168, 189, 252, 280, 315, 323, 378, 392, 420, 441, 525, 588, 630, 700, 735, 882, 899, 980, 1029, 1050, 1372, 1470, 1750, 1763, 2058, 2450, 2816, 3430, 3599, 3773, 4224, 4802, 5183, 5929, 6336, 7040, 9317, 9504, 9856, 10403

Offset: 1

Author

Jason Earls, Aug 02 2003

Keywords

• nonn

Examples

			112 is a term because 112 = 2^4*7 with 5 primes dividing it and 7-2=5.
		

Links

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

Crossrefs

Cf. A001222, A006530, A046665.

Programs

Magma

f:=func; [1] cat [k:k in [2..10000]| Max(PrimeDivisors(k))-Min(PrimeDivisors(k)) eq f(k)]; // Marius A. Burtea, Dec 16 2019

Mathematica

seqQ[1] = True; seqQ[n_] := Plus @@ Last /@ (f = FactorInteger[n]) == f[[-1, 1]] - f[[1, 1]]; Select[Range[10^4], seqQ] (* Amiram Eldar, Dec 16 2019 *)

PARI

print1("1, "); for(k=2,10500,my(f=factor(k));if(bigomega(k)==vecmax(f[, 1])-f[1,1],print1(k,", "))) \\ Hugo Pfoertner, Dec 16 2019

Extensions

Name edited by Hugo Pfoertner, Dec 16 2019