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A095408
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Total number of decimal digits in all distinct prime factors of n minus number of digits in n.
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4
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-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
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OFFSET
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1,66
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LINKS
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FORMULA
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(PARI)
A095407(n) = vecsum(apply(p->#digits(p), factor(n)[, 1]));
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CROSSREFS
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KEYWORD
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base,sign
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AUTHOR
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STATUS
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approved
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