A127171 Difference between largest prime factors of two successive 3-almost primes.

1, 0, 2, -2, 4, -2, 2, 4, -6, 0, 8, -6, 4, 6, -10, -2, 14, -6, 10, -16, 4, 6, -10, 4, 8, 10, -16, 18, -26, 8, 10, -16, 30, -20, -6, 30, -30, 6, 2, 24, -14, -22, 6, 18, 16, -28, -6, 10, 30, -16, -14, -12, 48, -42, -6, 50, -54, 34, -24, 26, -14, -10, 48, -54, -2, 20, 16, 24, -52, -6, 16, 44, -42, 48, -26, -30, -10, 70, -46, -24, -6, 16

Offset

1,3

Links

Table of n, a(n) for n=1..82.

Formula

a(n) = A006530(A014612(n+1)) - A006530(A014612(n)).

Example

a(1) = 1 because 3-almostprime(1) = 8 and 3-almostprime(2) = 12, greatest prime factor(12) = 3, greatest prime factor(8) = 2 and 3-2 = 1.
a(3) = gpf(20) - gpf(18) = 5 - 3 = 2.
a(4) = gpf(27) - gpf(20) = 3 - 5 = -2.

Maple

A014612 := proc(nmax) local a, n; a := [8] ; while nops(a) < nmax do n := op(-1, a)+1 ; while numtheory[bigomega](n) <> 3 do n := n+1 ; od ; a := [op(a), n] ; od ; RETURN(a) ; end: A006530 := proc(n) op(1, op(-1, ifactors(n)[2])) ; end: A127171 := proc(nmax) local a, threeAlm, i ; threeAlm := A014612(nmax) ; a := [] ; for i from 2 to nops(threeAlm) do a := [op(a), A006530(op(i, threeAlm))-A006530(op(i-1, threeAlm)) ] ; od ; RETURN(a) ; end: A127171(100) ; # R. J. Mathar, Apr 01 2007

Mathematica

Last[#]-First[#]&/@(Partition[FactorInteger[#][[-1, 1]]&/@Select[Range[ 500], PrimeOmega[#]==3&], 2, 1]) (* Harvey P. Dale, May 30 2014 *)

Crossrefs

Cf. A014612, A126663.

Sequence in context: A143230 A276604 A072301 * A215655 A118232 A115070

Adjacent sequences: A127168 A127169 A127170 * A127172 A127173 A127174

Keyword

easy,sign

Author

Jonathan Vos Post, Mar 25 2007

Extensions

More terms from R. J. Mathar, Apr 01 2007

Status

approved