A090341 Difference between the sums of the prime factors, including multiplicity, of n and those of n + 2.

-3, -2, -2, -1, -2, -1, 1, -1, -5, 0, -2, -2, 5, 1, -9, 0, -2, -1, 9, -4, -13, 4, 13, -6, 1, 4, -20, 1, -2, 0, 17, -9, 2, 9, -25, -11, 21, 10, -25, -1, -2, -3, 32, -10, -36, 14, 33, -1, -6, -5, -33, 6, 37, -2, -6, -18, -37, 19, -2, -21, 48, 21, -5, -4, -49, -5, 41, 7, -45, 2, -2, -27, 60, 16, -5, 5, -61, 5, 67, -30, -71, 29, 61, -31, -10

Offset: 1

Author

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

Keywords

• sign

Examples

			a(24)=-6 because 24=2*2*2*3, 26=2*13 and (2+2+2+3)-(2+13)=-6.
		

Crossrefs

Cf. A001414, A090340, A090342, A090343.

Programs

Mathematica

Join[{-3},#[[1]]-#[[3]]&/@Partition[Table[Total[Flatten[Table[#[[1]], #[[2]]]& /@ FactorInteger[n]]],{n,2,90}],3,1]] (* Harvey P. Dale, Apr 06 2018 *)

Formula

a(n) = A001414(n) - A001414(n+2). - Wesley Ivan Hurt, Aug 29 2016