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 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]. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n) = A034699(n) - A002034(n). EXAMPLE a(18) = 3 since 18 is a factor of 6!, 9 is the largest prime power factor of 18 and 9-6=3. PROG (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 CROSSREFS Cf. A002034, A034699, A057108, A057111. Sequence in context: A277578 A089331 A125856 * A073275 A309528 A293496 Adjacent sequences: A057107 A057108 A057109 * A057111 A057112 A057113 KEYWORD easy,nonn AUTHOR Henry Bottomley, Aug 08 2000 EXTENSIONS More terms added and term a(90) corrected from 4 to 3 by Antti Karttunen, Jul 22 2018 STATUS approved

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Last modified March 25 23:47 EDT 2023. Contains 361529 sequences. (Running on oeis4.)