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Search: id:A111359
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| A111359 |
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Positive integers n such that the difference between the n-th prime and the sum of the divisors of n is congruent to 1 (mod n). |
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+0
1
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| 3, 6, 9, 10, 13, 42, 73, 184, 511, 690, 3275, 18918, 20574, 21340, 44140, 116669, 543214, 567016, 637321, 688792, 878649, 2582446, 27067133
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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n's such that (prime_n - sigma(n))== 1 (mod n); A000040(n)-A000203(n)==1 (mod n). - Robert G. Wilson v (rgwv(at)rgwv.com), Nov 09 2005
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EXAMPLE
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The 42nd prime is 181. The divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42 and their sum is 96. 181-96 = 85. 85 = 1 mod 42.
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MATHEMATICA
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Select[Range[10^8], Mod[Prime[ # ] - Plus @@ Divisors[ # ], # ] == 1 &] (*Chandler*)
fQ[n_] := Mod[Prime[n] - DivisorSigma[1, n], n] == 1; t = {}; Do[ If[ fQ[n], AppendTo[t, n]], {n, 50000000}]; t (* Robert G. Wilson v *)
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CROSSREFS
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Adjacent sequences: A111356 A111357 A111358 this_sequence A111360 A111361 A111362
Sequence in context: A055264 A113502 A061904 this_sequence A085782 A085780 A107084
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KEYWORD
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more,nonn
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AUTHOR
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Ray G. Opao (1260(AT)email.com), Nov 07 2005
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EXTENSIONS
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a(22) and a(23) from Ray Chandler (rayjchandler(AT)sbcglobal.net) and Robert G. Wilson v (rgwv(at)rgwv.com), Nov 09 2005
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