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A057110
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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].
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4
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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
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OFFSET
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1,8
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..65537
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FORMULA
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a(n) = A034699(n) - A002034(n).
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EXAMPLE
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a(18) = 3 since 18 is a factor of 6!, 9 is the largest prime power factor of 18 and 9-6=3.
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PROG
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(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
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CROSSREFS
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Cf. A002034, A034699, A057108, A057111.
Sequence in context: A277578 A089331 A125856 * A073275 A309528 A293496
Adjacent sequences: A057107 A057108 A057109 * A057111 A057112 A057113
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley, Aug 08 2000
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EXTENSIONS
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More terms added and term a(90) corrected from 4 to 3 by Antti Karttunen, Jul 22 2018
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STATUS
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approved
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