cp's OEIS Frontend

A084317 Concatenation of the prime factors of n, in increasing order.

%I A084317 #30 Mar 26 2020 18:01:27
%S A084317 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,
%T A084317 213,3,27,29,235,31,2,311,217,57,23,37,219,313,25,41,237,43,211,35,
%U A084317 223,47,23,7,25,317,213,53,23,511,27,319,229,59,235,61,231,37,2,513,2311,67
%N A084317 Concatenation of the prime factors of n, in increasing order.
%C A084317 Prime factor set of n is concatenated as follows:
%C A084317 1. factorize n;
%C A084317 2. order prime factors without exponents in order of magnitude;
%C A084317 3. concatenate digits to get a(n) as a decimal number.
%C A084317 The choice a(1)=0 is conventional; a(1)=1 would have been another possible choice. - _M. F. Hasler_, Oct 21 2014
%H A084317 Alois P. Heinz, <a href="/A084317/b084317.txt">Table of n, a(n) for n = 1..10000</a>
%F A084317 a(n) = a(squarefree kernel of n) = a(n^k) for any power k >= 1.
%e A084317 a(1) = 0 since 1 has no prime factors to concatenate.
%e A084317 n = 2520 = 2*2*2*3*3*5*7; prime factor set = {2,3,5,7}, so a(2520) = 2357.
%p A084317 with(numtheory):
%p A084317 a:= n-> parse(cat(`if`(n=1, 0, sort([factorset(n)[]])[]))):
%p A084317 seq(a(n), n=1..100);  # _Alois P. Heinz_, Dec 06 2014
%t A084317 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}]
%t A084317 {0}~Join~Table[FromDigits@ Flatten@ IntegerDigits@ Map[First, FactorInteger@ n], {n, 2, 67}] (* _Michael De Vlieger_, May 02 2016 *)
%o A084317 (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
%Y A084317 Cf. A084318, A084319.
%K A084317 base,nonn,look
%O A084317 1,2
%A A084317 _Labos Elemer_, Jun 16 2003
%E A084317 Edited by _M. F. Hasler_, Oct 21 2014