A180876 a(n) = sopfr(n) - (floor(sqrt(n))*bigomega(n)).

0, 1, 2, 0, 3, 1, 5, 0, 0, 1, 8, -2, 10, 3, 2, -8, 13, -4, 15, -3, 2, 5, 19, -7, 0, 5, -6, -4, 24, -5, 26, -15, 4, 9, 2, -14, 31, 9, 4, -13, 35, -6, 37, -3, -7, 13, 41, -19, 0, -9, 6, -4, 46, -17, 2, -15, 8, 17, 52, -16, 54, 19, -8, -36, 2, -8, 59, -3, 10, -10, 63, -28, 65, 23, -11

Offset

1,3

Comments

Prime factors totaled with multiplicity. - Harvey P. Dale, Jun 22 2025

Links

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

Example

Take the number 287. Find the floor of its square root: sqrt(287)=16.941074... it's 16. Now get the factors of 287 = 7*41. Subtract the first prime factor from the floor of the square root: 7-16 = -9. Now subtract the second prime factor from the floor of the square root: 41-16 = 25. Add those values together: -9+25 = 16. It's the same as the floor of the square root. But it doesn't always work out that way.

Mathematica

Join[{0}, Table[Total[Times@@@FactorInteger[n]]-Floor[Sqrt[n]]PrimeOmega[n], {n, 2, 80}]] (* Harvey P. Dale, Jun 22 2025 *)

Crossrefs

Sequence in context: A162517 A392489 A391843 * A162170 A266770 A282892

Adjacent sequences: A180873 A180874 A180875 * A180877 A180878 A180879

Keyword

easy,sign

Author

Jason Earls, Sep 23 2010

Status

approved