|
%I #18 Jun 27 2024 22:15:31
%S 0,1,0,3,0,2,4,1,0,1,8,3,2,3,10,5,0,14,6,16,6,7,8,20,10,4,12,12,12,26,
%T 6,28,12,14,16,34,18,19,10,0,18,38,40,12,20,44,22,2,24,21,26,25,50,16,
%U 26,0,56,29,58,32,6,33,1,35,22,36,34,8,68,35,38,24,34,70,4,35,42,76,6,0
%N Absolute difference between prime factors of n-th semiprime mod n.
%H Alois P. Heinz, <a href="/A178313/b178313.txt">Table of n, a(n) for n = 1..20000</a>
%e a(2)=1 because semiprime(2) = 6 = 3*2 and (3-2) mod 2 = 1.
%t semiPrimeQ[n_] := Plus @@ Last /@ FactorInteger@ n == 2; f[n_] := Subtract @@ Reverse@ Flatten[ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@ n]; t = Select[ Range@ 215, semiPrimeQ]; Table[ Mod[ f[ t[[n]]], n], {n, 80}]
%t f[{a_,b_}]:=Module[{c=FactorInteger[b][[;;,1]]},If[Length[c]==1,0,Mod[Differences[c][[1]],a]]]; Module[{nn=300,spr},spr=Select[Range[nn],PrimeOmega[#]==2&];f/@Thread[{Range[ Length[ spr]],spr}]] (* _Harvey P. Dale_, May 29 2024 *)
%Y Cf. A001358, A178102, A109313.
%K nonn
%O 1,4
%A _Juri-Stepan Gerasimov_, Dec 20 2010
|
