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A084317
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Concatenation of the prime factors of n, in increasing order.
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24
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0, 2, 3, 2, 5, 23, 7, 2, 3, 25, 11, 23, 13, 27, 35, 2, 17, 23, 19, 25, 37, 211, 23, 23, 5, 213, 3, 27, 29, 235, 31, 2, 311, 217, 57, 23, 37, 219, 313, 25, 41, 237, 43, 211, 35, 223, 47, 23, 7, 25, 317, 213, 53, 23, 511, 27, 319, 229, 59, 235, 61, 231, 37, 2, 513, 2311, 67
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OFFSET
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1,2
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COMMENTS
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Prime factor set of n is concatenated as follows:
1. factorize n;
2. order prime factors without exponents in order of magnitude;
3. concatenate digits to get a(n) as a decimal number.
The choice a(1)=0 is conventional; a(1)=1 would have been another possible choice. - M. F. Hasler, Oct 21 2014
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LINKS
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FORMULA
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a(n) = a(squarefree kernel of n) = a(n^k) for any power k >= 1.
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EXAMPLE
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a(1) = 0 since 1 has no prime factors to concatenate.
n = 2520 = 2*2*2*3*3*5*7; prime factor set = {2,3,5,7}, so a(2520) = 2357.
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MAPLE
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with(numtheory):
a:= n-> parse(cat(`if`(n=1, 0, sort([factorset(n)[]])[]))):
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MATHEMATICA
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ffi[x_] := Flatten[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] lf[x_] := Length[FactorInteger[x]] nd[x_, y_] := 10*x+y tn[x_] := Fold[nd, 0, x] conc[x_] := Fold[nd, 0, Flatten[IntegerDigits[ba[x]], 1]] Table[conc[w], {w, 1, 128}]
{0}~Join~Table[FromDigits@ Flatten@ IntegerDigits@ Map[First, FactorInteger@ n], {n, 2, 67}] (* Michael De Vlieger, May 02 2016 *)
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PROG
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(PARI) A084317(n)=if(n>1, eval(concat(apply(t->Str(t), factor(n)[, 1]~)))) \\ Unfortunately up to PARI version 2.7.1 at least, "Str" cannot be applied as a closure (= function), but Str = Str() = "". - M. F. Hasler, Oct 22 2014
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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