A109313 - OEIS

%I #27 Feb 06 2017 20:16:11

%S 0,1,0,3,5,2,4,9,0,11,8,15,2,17,10,21,0,14,6,16,27,29,8,20,35,4,39,12,

%T 41,26,6,28,45,14,51,34,18,57,10,0,59,38,40,12,65,44,69,2,24,71,26,77,

%U 50,16,81,0,56,87,58,32,6,95,64,99,22,36,101,8,68,105,38,24,107,70,4

%N Difference between prime factors of n-th semiprime.

%C a(n)=0 iff sp(n) is a square of prime, sp(n) = n-th semiprime = A001358(n).

%H Alois P. Heinz, <a href="/A109313/b109313.txt">Table of n, a(n) for n = 1..20000</a> (first 1000 terms from Zak Seidov)

%e a(1)=0 because sp(1)=4=2*2 and 2-2=0; a(2)=1 because sp(2)=6=2*3 and 3-2=1; sp(n)=n-th semiprime.

%p with(numtheory): a:=proc(n) if bigomega(n)=2 and nops(factorset(n))=2 then factorset(n)[2]-factorset(n)[1] elif bigomega(n)=2 then 0 else fi end: seq(a(n),n=1..225); # _Emeric Deutsch_

%p # second Maple program:

%p b:= proc(n) option remember; local k;

%p       if n=1 then 4

%p     else for k from 1+b(n-1) do if not isprime(k) and

%p             numtheory[bigomega](k)=2 then return k fi

%p          od

%p       fi

%p     end:

%p a:= n-> (s-> max(s)-min(s))(numtheory[factorset](b(n))):

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Feb 05 2017

%t spQ[n_] := PrimeOmega[n] == 2; fi[n_] := FactorInteger[n];

%t f[n_] := fi[n][[-1, 1]] - fi[n][[1, 1]];

%t f[#] & /@ Select[Range@215, spQ] (* _Zak Seidov_, Oct 16 2014 *)

%Y Cf. A001358, A068318, A178313.

%K nonn

%O 1,4

%A _Zak Seidov_, Jun 27 2005

%E Edited by _Zak Seidov_, Oct 16 2014