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Terms of A123856 that are not terms of A124273.
2

%I #11 Oct 21 2018 06:24:29

%S 2,5,181

%N Terms of A123856 that are not terms of A124273.

%C Primes that divide A123855(p-1) = Sum_{j=1..p-1} Sum_{i=1..p-1} prime(i)^j but not A124271(p) = Sum_{i=1..p} (prime(i)^p - 1)/(prime(i) - 1).

%C The next term if it exists is greater than 1000.

%C The next term A124275(4), if it exists, is larger than 25000. (Checked by calculating sequences A123856 and A124273 to 1200 terms.) - _M. F. Hasler_, Nov 10 2006

%e A123856(n) begins {2, 3, 5, 7, 13, 17, 19, 31, 47, 59, 61, 71, 101, 103, 107, 109, 137, 149, 151, 157, 167, 181, 197, ...}.

%e A124273(n) begins {3, 7, 13, 17, 19, 31, 47, 59, 61, 71, 101, 103, 107, 109, 137, 149, 151, 157, 167, 197, ...}.

%e Thus a(1) = 2, a(2) = 5, a(3) = 181.

%p A124275:=proc(n) option remember; local i1,i2; i1:=1:i2:=1: # find index i1 such that A123856[i1] is > A124275[n-1]; # then continue until A124273 "jumped over" the term A123856[i1] # while n>1 and A123856(i1) <= procname(n-1) or A123856(i1) = A124273(i2) do i1:=i1+1: # find index i2 such that A124273[i2] is >= A123856(i1) # while A124273(i2) < A123856(i1) do i2:=i2+1: od: od: A123856(i1) end; # _M. F. Hasler_, Nov 10 2006

%Y Cf. A123855, A123856, A124271, A124273.

%K bref,hard,more,nonn

%O 1,1

%A _Alexander Adamchuk_, Oct 23 2006