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 A109313 Difference between prime factors of n-th semiprime. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 12 07:57 EDT 2024. Contains 375850 sequences. (Running on oeis4.)