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Search: id:A118219
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| A118219 |
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Smallest number k>1 such that Sum_{i=1..k} Prime[i]^n divides Product_{i=1..k} Prime[i]^n. |
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1
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OFFSET
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1,1
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EXAMPLE
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a(1) = 3 because 2 + 3 + 5 = 10 divides 2*3*5 = 30 but 2 + 3 = 5 does not divide 2*3 = 6.
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MATHEMATICA
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f[n_] := Block[{k = 2, p = 2, s = 2^n}, While[p = p*Prime@ k; s = s + Prime@ k^n; PowerMod[p, n, s] != 0, k++ ]; k]; Do[ Print@ f@n, {n, 10}] (Robert G. Wilson v)
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CROSSREFS
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Cf. A051838 = Sum of first n primes divides product of first n primes. Cf. A125314 = Smallest number k>1 such that Sum_{i=1..k} i^n divides Product_{i=1..k} i^n. Cf. A007504, A002110, A024450, A098999, A122102, A122103.
Sequence in context: A078242 A108739 A072973 this_sequence A077679 A045863 A121023
Adjacent sequences: A118216 A118217 A118218 this_sequence A118220 A118221 A118222
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KEYWORD
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hard,more,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 24 2007
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EXTENSIONS
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a(6) from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 02 2007
a(7)>991430. - Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 02 2007
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