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Search: id:A097649
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| A097649 |
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a(n) is the smallest number m such that phi(m)=10^n. |
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+0
2
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| 1, 11, 101, 1111, 10291, 100651, 1004251, 10165751, 100064101, 1000078501, 10000222501, 100062501601, 1000062516001, 10000062660001, 100002441447211, 1003922328562757, 10000390625025601, 100000002482366251
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OFFSET
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0,2
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COMMENT
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phi(1)=1, phi(11)=10 & for n > 0 phi(25*10^n)=10^(n+1), so for each n, a(n) exists and is less than 25*10^(n-1)+1.
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EXAMPLE
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a(10)=10000222501 because phi(10000222501)=10^10 and for all m<10000222501 phi(m) # 10^10.
a(15)=1003922328562757 because of the primes among the divisors plus 1 of 10^15, they being {2, 3, 5, 11, 17, 41, 101, 251, 257, 401, 641, 1601, 4001, 16001, 25601, 40961, 62501, 160001, 62500001, 2441406251, 2500000001}, the least product of all the possible subsets whose totient equals 10^15 is a(15).
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MATHEMATICA
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a[n_] := Block[{m = 10^n}, While[ EulerPhi[m] != 10^n, m++ ]; m]; Do[ Print[ a[n]], {n, 0, 12}]
(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := If[n == 0, 1, Block[{p = Select[ Divisors[10^n], PrimeQ[ # + 1] &]}, Min[ Transpose[ Partition[ Flatten[ Table[ Select[ Transpose[{Times @@@ KSubsets[p, i], Times @@@ KSubsets[p + 1, i]}], #[[1]] == 10^n &], {i, 9}]], 2]][[2]] ]]]; Table[ f[n], {n, 0, 18}] (from Robert G. Wilson v Mar 14 2005)
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CROSSREFS
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Cf. A097650.
Sequence in context: A113978 A006943 A073030 this_sequence A072075 A088292 A135563
Adjacent sequences: A097646 A097647 A097648 this_sequence A097650 A097651 A097652
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KEYWORD
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nonn
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AUTHOR
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Farideh Firoozbakht (mymontain(AT)yahoo.com), Sep 05 2004
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EXTENSIONS
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Edited and extended from a(11) by Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 12 2005
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