A046665 Largest prime divisor of n - smallest prime divisor of n (a(1)=0).

0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 5, 2, 0, 0, 1, 0, 3, 4, 9, 0, 1, 0, 11, 0, 5, 0, 3, 0, 0, 8, 15, 2, 1, 0, 17, 10, 3, 0, 5, 0, 9, 2, 21, 0, 1, 0, 3, 14, 11, 0, 1, 6, 5, 16, 27, 0, 3, 0, 29, 4, 0, 8, 9, 0, 15, 20, 5, 0, 1, 0, 35, 2, 17, 4, 11, 0, 3, 0, 39, 0, 5, 12, 41, 26, 9, 0

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

Even nonzero terms correspond to odd composite numbers that are not powers of primes. Terms of A030173 appear in this sequence infinitely often. - Alonso del Arte, Nov 27 2011

A135093(n) = first occurrence of A030173(n). - Reinhard Zumkeller, Jul 03 2015

References

• Handbook of Number Theory, D. S. Mitrinovic et al., Kluwer, Section IV.1.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006530, A020639, A074320, A066048, A130064, A130065.

Programs

Haskell

a046665 n = a006530 n - a020639 n  -- Reinhard Zumkeller, Jul 03 2015

Maple

a:= n-> `if`(n=1, 0, (s-> max(s)-min(s))(numtheory[factorset](n))):
seq(a(n), n=1..100);  # Alois P. Heinz, Mar 07 2020

Mathematica

f[n_]:=Transpose[FactorInteger[n]][[1]];Table[Last[f[n]-First[f[n]]],{n,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 08 2011 *)
lpd[n_]:=Module[{fi=FactorInteger[n]},fi[[-1,1]]-fi[[1,1]]]; Array[lpd,90] (* Harvey P. Dale, Dec 31 2017 *)

PARI

a(n)={if(n==1, 0, my(f=factor(n)[,1]); f[#f]-f[1])} \\ Andrew Howroyd, Mar 07 2020

Formula

a(n) = A006530(n) - A020639(n).

Extensions

More terms from James Sellers