A078142 a(n) is the sum of the differences of the distinct prime factors p of n and the next square larger than p.

0, 2, 1, 2, 4, 3, 2, 2, 1, 6, 5, 3, 3, 4, 5, 2, 8, 3, 6, 6, 3, 7, 2, 3, 4, 5, 1, 4, 7, 7, 5, 2, 6, 10, 6, 3, 12, 8, 4, 6, 8, 5, 6, 7, 5, 4, 2, 3, 2, 6, 9, 5, 11, 3, 9, 4, 7, 9, 5, 7, 3, 7, 3, 2, 7, 8, 14, 10, 3, 8, 10, 3, 8, 14, 5, 8, 7, 6, 2, 6, 1, 10, 17, 5, 12, 8, 8, 7, 11, 7, 5, 4, 6, 4, 10, 3, 3, 4

Offset: 1

Author

Jason Earls, Nov 20 2002

Keywords

• easy
• nonn

Comments

From Bernard Schott, Dec 05 2019: (Start)

a(n) = 1 iff n > 1 is a power of 3.

a(n) = 2 iff n > 1 is a power of p prime with p in A028871. (End)

Examples

			a(6)=3 because 6=2*3 and (4-2)+(4-3)=3.
a(20)=6 because 20=2^2*5 and (4-2)+(9-5)=6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Programs

Mathematica

f[n_]:=Module[{difs=Transpose[FactorInteger[n]][[1]]}, Total[Ceiling[ Sqrt[difs]]^2-difs]]; Array[f,120] (* Harvey P. Dale, Apr 18 2011 *)