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 A084317 Concatenation of the prime factors of n, in increasing order. 19
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 EXAMPLE 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. a(n) = a(squarefree kernel of n) = a(n^k) for any power k >= 1. MAPLE with(numtheory): a:= n-> parse(cat(`if`(n=1, 0, sort([factorset(n)[]])[]))): seq(a(n), n=1..100);  # Alois P. Heinz, Dec 06 2014 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A084318, A084319. Sequence in context: A133568 A120716 A084318 * A037279 A163591 A085307 Adjacent sequences:  A084314 A084315 A084316 * A084318 A084319 A084320 KEYWORD base,nonn,look AUTHOR Labos Elemer, Jun 16 2003 EXTENSIONS Edited by M. F. Hasler, Oct 21 2014 STATUS approved

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Last modified August 24 03:20 EDT 2019. Contains 326260 sequences. (Running on oeis4.)