A095408 Total number of decimal digits in all distinct prime factors of n minus number of digits in n.

-1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, -1, 0, 0, 1, 0, -1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, -1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, -1, 1, 2, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 2, 0, 0, -1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, -1

Offset: 1

Author

Labos Elemer, Jun 21 2004

Keywords

• base
• sign

Examples

			n=22: prime divisors are {2,11}, a(22) = 3-2 = 1.
n=63: prime divisors are {3,7}, a(63) = 2-2 = 0.
n=100: prime divisors are {2,5}, a(100) = 2-3 = -1.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12345

Crossrefs

Cf. A055642, A095407.

Programs

Mathematica

ffi[x_] :=Flatten[FactorInteger[x]] lf[x_] :=Length[FactorInteger[x]] ba[x_] :=Table[Part[ffi[x], 2*j-1], {j, 1, lf[x]}] tdp[x_] :=Flatten[Table[IntegerDigits[Part[ba[x], j]], {j, 1, lf[x]}], 1] pl[x_] :=Length[tdp[x]] nl[x_] :=Length[IntegerDigits[x]] t1=Table[nl[w], {w, 1, 1000}];t2=Table[pl[w], {w, 1, 1000}];t2-t1
(* Second program: *)
Array[Total@ IntegerLength[FactorInteger[#][[All, 1]]] - IntegerLength@ # - Boole[# == 1] &, 108] (* Michael De Vlieger, Dec 16 2017 *)

PARI

A095407(n) = vecsum(apply(p->#digits(p), factor(n)[, 1]));
A095408(n) = (A095407(n) - #digits(n)); \\ Antti Karttunen, Dec 16 2017

Formula

a(n) = A095407(n) - A055642(n).