A090342 Difference between the sums of the prime factors, including multiplicity, of n and those of n + 3.

-4, -3, -2, -3, -1, -1, 0, -5, -1, -6, 2, -1, 5, -8, 0, -11, 8, -2, 6, -14, 1, 3, 8, 0, -1, -14, -1, -20, 19, -4, 12, -2, 4, -18, -9, -6, 26, -20, 4, -32, 26, 1, 18, -32, 0, 11, 35, -9, -3, -41, 9, 1, 40, -11, -15, -46, 10, -30, 26, -1, 49, 15, -3, -55, -3, -10, 53, -50, 14, -59, 32, -1, 50, 21, -5, -56, 5, 6, 36, -70, -2, 21, 38

Offset: 1

Author

Charles K. Layman (cklayman(AT)juno.com), Nov 25 2003

Keywords

• sign

Examples

			a(24)=0 because 24=2*2*2*3, 27=3*3*3 and (2+2+2+3)-(3+3+3)=0.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001414, A090340, A090341, A090343.

Programs

Mathematica

Join[{-4},#[[1]]-#[[4]]&/@(Partition[Table[Total[Flatten[Table[#[[1]], #[[2]]]&/@ FactorInteger[n]]],{n,2,90}],4,1])] (* Harvey P. Dale, Sep 16 2018 *)

Formula

a(n) = A001414(n) - A001414(n+3). - Wesley Ivan Hurt, Aug 29 2016