A382468 a(n) = (largest prime factor of n) minus (its remaining distinct prime factors).

2, 3, 2, 5, 1, 7, 2, 3, 3, 11, 1, 13, 5, 2, 2, 17, 1, 19, 3, 4, 9, 23, 1, 5, 11, 3, 5, 29, 0, 31, 2, 8, 15, 2, 1, 37, 17, 10, 3, 41, 2, 43, 9, 2, 21, 47, 1, 7, 3, 14, 11, 53, 1, 6, 5, 16, 27, 59, 0, 61, 29, 4, 2, 8, 6, 67, 15, 20, 0, 71, 1, 73, 35, 2, 17, 4, 8, 79, 3, 3

Offset: 2

Author

Paolo Xausa, Mar 31 2025

Keywords

• sign
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A212665 (positions of negative terms), A215142 (positions of ones), A382469 (positions of zeros).

Cf. A006530, A008472, A027748.

Programs

Maple

A382468 := proc(n)
    2*A006530(n)-A008472(n) ;
end proc:
seq( A382468(n),n=1..50) ; # R. J. Mathar, Apr 01 2025

Mathematica

A382468[n_] := Last[#] - Total[Most[#]] & [FactorInteger[n][[All, 1]]];
Array[A382468, 100, 2]

Formula

a(p) = p, for p prime.

a(n) = 2*A006530(n) - A008472(n).