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Search: id:A123856
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| A123856 |
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Primes p that divide A123855[p-1] = Sum[ Sum[ Prime[i]^j, {i,1,p-1}], {j,1,p-1}]. |
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9
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| 2, 3, 5, 7, 13, 17, 19, 31, 47, 59, 61, 71, 101, 103, 107, 109, 137, 149, 151, 157, 167, 181, 197, 211, 223, 227, 229, 269, 317, 337, 349, 353, 379, 383, 389, 401, 421, 439, 449, 457, 463, 479, 521, 523, 541, 547, 563, 569, 571, 587, 599, 613, 617, 631, 643
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A123855[n] = Sum[ Sum[ Prime[i]^j, {i,1,n}], {j,1,n}]. Prime p = a(n) divides A123855[p-1]. Nonprime numbers n that divide A123855(n-1) are listed in A123857[n] = {4,8,16,32,38,64,128,205,256,316,512,...}. It appears that 2^k divides A123855(2^k-1) for all k>0 (confirmed for 0<k<10).
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LINKS
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M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 10 2006, Table of n, a(n) for n = 1..199
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MAPLE
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A123855_mod := proc(n, p) option remember; local s, i, pi; s:=0: for i to n do pi:= ithprime(i) mod p: if pi=1 then s:=s+n mod p: else s := s+pi*(pi &^ n - 1)/(pi-1) mod p fi od end; A123856 := proc(n::posint) option remember; local p; if n>1 then p:=nextprime( procname(n-1)) else p:=2 fi: while A123855_mod(p-1, p)<>0 do p:=nextprime( p ) od: p end; - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 10 2006
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MATHEMATICA
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Do[p=Prime[n]; f=Mod[Sum[Sum[PowerMod[Prime[i], j, p], {i, 1, p-1}], {j, 1, p-1}], p]; If[f==0, Print[p]], {n, 1, 150}]
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CROSSREFS
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Cf. A123857, A123855 = Sum[ Sum[ Prime[i]^j, {i, 1, n}], {j, 1, n}]. Cf. A086787 - Sum(Sum(i^j, j=1..n), i=1..n).
Sequence in context: A049587 A038903 A136003 this_sequence A120857 A000043 A109799
Adjacent sequences: A123853 A123854 A123855 this_sequence A123857 A123858 A123859
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 13 2006
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