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A078142 a(n) is the sum of the differences of the distinct prime factors p of n and the next square larger than p. 9
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 22 18:03 EST 2020. Contains 332148 sequences. (Running on oeis4.)