A057108 Difference between the smallest number S(n) with S(n)! a multiple of n and the largest prime factor of n [taking a(1)=0].

0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 1, 0, 0, 0, 4, 0, 3, 0, 0, 0, 0, 0, 1, 5, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 3, 7, 5, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 5, 0, 0, 0, 0, 1, 6, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 7, 0, 5, 0, 0, 0, 0, 0

Offset: 1

Author

Henry Bottomley, Aug 08 2000

Keywords

• easy
• nonn

Examples

			a(12)=1 since 12 is a factor of 4!, 3 is the largest prime factor of 12 and 4-3=1
		

References

• Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 284-292.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Steven R. Finch, The Average Value of the Smarandache Function [Broken link]
• Steven R. Finch, The Average Value of the Smarandache Function

Crossrefs

Cf. A002034, A006530, A057109, A057110.

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.
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1); \\ From A006530.
A057108(n) = (A002034(n) - A006530(n)); \\ Antti Karttunen, Jul 22 2018

Formula

a(n) = A002034(n) - A006530(n).

Extensions

More terms from James Sellers, Aug 22 2000