A124238 Terms of A123857 that are not powers of 2.
38, 205, 316, 736, 3776, 4916, 5888, 7736, 11138, 22287, 23308, 23924, 39538, 62336, 71936
Offset: 1
Extensions
More terms from Max Alekseyev, Sep 13 2009
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a(1) = prime(1)^1 = 2. a(2) = prime(1)^1 + prime(1)^2 + prime(2)^1 + prime(2)^2 = 2^1 + 2^2 + 3^1 + 3^2 = 18.
[(&+[ (&+[ NthPrime(i)^j: j in [1..n]]): i in [1..n]]): n in [1..20]]; // G. C. Greubel, Aug 08 2019
A123855 := p-> sum((ithprime(i)^p-1)/(ithprime(i)-1)*ithprime(i),i = 1 .. p); map(%,[$1..20]); # M. F. Hasler, Nov 09 2006
Table[Sum[Sum[Prime[i]^j,{i,1,n}],{j,1,n}],{n,1,20}]
vector(20, n, sum(i=1,n, sum(j=1,n, prime(i)^j )) ) \\ G. C. Greubel, Aug 08 2019
[sum(sum( nth_prime(i)^j for j in (1..n)) for i in (1..n)) for n in (1..20)] # G. C. Greubel, Aug 08 2019
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, Nov 10 2006
fQ[p_] := Mod[ Sum[ PowerMod[ Prime@ i, j, p], {j, p - 1}, {i, p - 1}], p] == 0; Select[ Prime@ Range@ 117, fQ] (* Robert G. Wilson v, Jun 10 2011 *)
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