A192133 Difference of base and exponent of prime powers (cf. A000961).

1, 1, 2, 0, 4, 6, -1, 1, 10, 12, -2, 16, 18, 22, 3, 0, 28, 30, -3, 36, 40, 42, 46, 5, 52, 58, 60, -4, 66, 70, 72, 78, -1, 82, 88, 96, 100, 102, 106, 108, 112, 9, 2, 126, -5, 130, 136, 138, 148, 150, 156, 162, 166, 11, 172, 178, 180, 190, 192, 196, 198, 210

Offset: 1

Author

Reinhard Zumkeller, Jun 26 2011

Keywords

• sign

Comments

a(1) = 1 by convention, in accordance with A025473(1) = 1 and A025474(1) = 0.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

A006093 and A090076 are subsequences.

Cf. A000961, A025473, A025474, A192134.

Programs

Mathematica

s[n_] := Module[{f = FactorInteger[n]}, If[Length[f] == 1, f[[1, 1]] - f[[1, 2]], Nothing]]; s[1] = 1; Array[s, 250] (* Amiram Eldar, May 16 2025 *)

Formula

a(n) = A025473(n)-A025474(n) = A192134(n)*A025473(n)/A000961(n).