A057110 Difference between largest prime power factor of n and the smallest number S(n) with S(n)! a multiple of n [taking a(1)=0].

0, 0, 0, 0, 0, 0, 0, 4, 3, 0, 0, 0, 0, 0, 0, 10, 0, 3, 0, 0, 0, 0, 0, 4, 15, 0, 18, 0, 0, 0, 0, 24, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 10, 35, 15, 0, 0, 0, 18, 0, 1, 0, 0, 0, 0, 0, 0, 2, 56, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 15, 0, 0, 0, 0, 10, 72, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 24, 0, 35, 0, 15, 0, 0, 0, 0, 0

Offset: 1

Author

Henry Bottomley, Aug 08 2000

Keywords

• easy
• nonn

Examples

			a(18) = 3 since 18 is a factor of 6!, 9 is the largest prime power factor of 18 and 9-6=3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A002034, A034699, A057108, A057111.

Programs

PARI

A002034(n) = if(1==n,n,my(s=factor(n)[, 1], k=s[#s], f=Mod(k!, n)); while(f, f*=k++); (k)); \\ After code in A002034.
A034699(n) = if(1==n,n,my(f=factor(n)); vecmax(vector(#f[, 1], i, f[i, 1]^f[i, 2]))); \\ After code in A034699.
A057110(n) = (A034699(n) - A002034(n)); \\ Antti Karttunen, Jul 22 2018

Formula

a(n) = A034699(n) - A002034(n).

Extensions

More terms added and term a(90) corrected from 4 to 3 by Antti Karttunen, Jul 22 2018