A109313 Difference between prime factors of n-th semiprime.

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, 41, 26, 6, 28, 45, 14, 51, 34, 18, 57, 10, 0, 59, 38, 40, 12, 65, 44, 69, 2, 24, 71, 26, 77, 50, 16, 81, 0, 56, 87, 58, 32, 6, 95, 64, 99, 22, 36, 101, 8, 68, 105, 38, 24, 107, 70, 4

Offset

1,4

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000 (first 1000 terms from Zak Seidov)

Example

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.

Maple

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
# second Maple program:
b:= proc(n) option remember; local k;
      if n=1 then 4
    else for k from 1+b(n-1) do if not isprime(k) and
            numtheory[bigomega](k)=2 then return k fi
         od
      fi
    end:
a:= n-> (s-> max(s)-min(s))(numtheory[factorset](b(n))):
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 05 2017

Mathematica

spQ[n_] := PrimeOmega[n] == 2; fi[n_] := FactorInteger[n];
f[n_] := fi[n][[-1, 1]] - fi[n][[1, 1]];
f[#] & /@ Select[Range@215, spQ] (* Zak Seidov, Oct 16 2014 *)

Crossrefs

Cf. A001358, A068318, A178313.

Sequence in context: A163364 A336760 A082822 * A331526 A176881 A065188

Adjacent sequences: A109310 A109311 A109312 * A109314 A109315 A109316

Keyword

nonn

Author

Zak Seidov, Jun 27 2005

Extensions

Edited by Zak Seidov, Oct 16 2014

Status

approved