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A345312
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a(n) = Sum_{p|n} (n/p)^gcd(p,n/p).
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0
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0, 1, 1, 4, 1, 5, 1, 16, 27, 7, 1, 40, 1, 9, 8, 64, 1, 225, 1, 104, 10, 13, 1, 152, 3125, 15, 729, 200, 1, 31, 1, 256, 14, 19, 12, 2052, 1, 21, 16, 408, 1, 41, 1, 488, 3384, 25, 1, 592, 823543, 100025, 20, 680, 1, 5859, 16, 792, 22, 31, 1, 932, 1, 33, 9270, 1024, 18, 61, 1
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OFFSET
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1,4
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COMMENTS
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a(p) = Sum_{p|p} (p/p)^gcd(p,p/p) = 1^1 = 1 for primes p.
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LINKS
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EXAMPLE
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a(10) = Sum_{p|10} (10/p)^gcd(p,10/p) = 5^gcd(2,5) + 2^gcd(5,2) = 5^1 + 2^1 = 7.
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MATHEMATICA
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Table[Sum[(n/k)^GCD[k, n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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