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A071786 In prime factorization of n replace each prime with its reversal (in decimal notation).

%I A071786 #37 Oct 12 2024 14:41:07
%S A071786 1,2,3,4,5,6,7,8,9,10,11,12,31,14,15,16,71,18,91,20,21,22,32,24,25,62,
%T A071786 27,28,92,30,13,32,33,142,35,36,73,182,93,40,14,42,34,44,45,64,74,48,
%U A071786 49,50,213,124,35,54,55,56,273,184,95,60,16,26,63,64,155,66,76,284,96,70,17,72
%N A071786 In prime factorization of n replace each prime with its reversal (in decimal notation).
%C A071786 The range of A007500 is a subset of the range of this sequence. - _Reinhard Zumkeller_, Jul 06 2009
%C A071786 Prime factors counted with multiplicity. - _Harvey P. Dale_, Jul 08 2017
%H A071786 N. J. A. Sloane, <a href="/A071786/b071786.txt">Table of n, a(n) for n = 1..10000</a>
%H A071786 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F A071786 Completely multiplicative with a(p) = A004086(p), p prime.
%F A071786 a(A000040(n)) = A004087(n).
%e A071786 a(143) = a(11*13) = a(11)*a(13) = 11*31 = 341.
%p A071786 read("transforms") ; A071786 := proc(n) local ifs, a, d ; ifs := ifactors(n)[2] ; a := 1 ; for d in ifs do a := a*digrev(op(1, d))^op(2, d) ; od: a ; end: # _R. J. Mathar_, Jun 16 2009
%p A071786 # second Maple program:
%p A071786 r:= n-> (s-> parse(cat(seq(s[-i], i=1..length(s)))))(""||n):
%p A071786 a:= n-> mul(r(i[1])^i[2], i=ifactors(n)[2]):
%p A071786 seq(a(n), n=1..100);  # _Alois P. Heinz_, Jun 19 2017
%t A071786 Table[Times@@IntegerReverse/@Flatten[Table[#[[1]],#[[2]]]&/@ FactorInteger[ n]],{n,80}] (* _Harvey P. Dale_, Jul 08 2017 *)
%o A071786 (Haskell)
%o A071786 a071786 = product . map a004086 . a027746_row
%o A071786 -- _Reinhard Zumkeller_, Oct 14 2011
%o A071786 (Python)
%o A071786 from sympy import factorint
%o A071786 from operator import mul
%o A071786 from functools import reduce
%o A071786 def A071786(n):
%o A071786     return 1 if n==1 else reduce(mul,(int(str(p)[::-1])**e for p,e in factorint(n).items())) # _Chai Wah Wu_, Aug 14 2014
%o A071786 (PARI) rev(n)=fromdigits(Vecrev(digits(n)))
%o A071786 a(n)=my(f=factor(n)); prod(i=1,#f~,rev(f[i,1])^f[i,2]) \\ _Charles R Greathouse IV_, Jun 28 2015
%Y A071786 Cf. A151764, A161594, A151765. For records see A151766, A151767.
%Y A071786 Cf. A151768 (complement), A376858 (fixed points).
%Y A071786 Cf. A027746.
%K A071786 nonn,base,mult,look
%O A071786 1,2
%A A071786 _Reinhard Zumkeller_, Jun 06 2002