A046665 - OEIS

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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

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OFFSET

1,10

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

FORMULA

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

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 *)