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

1,2

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)

Links

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

Example

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.

Mathematica

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

Crossrefs

Sequence in context: A091173 A101897 A208058 * A133422 A331136 A099312

Adjacent sequences: A078139 A078140 A078141 * A078143 A078144 A078145

Keyword

easy,nonn

Author

Jason Earls, Nov 20 2002

Status

approved