OFFSET
1,2
COMMENTS
Might be called TITO(n), turning n inside out then turning outside in.
Here is the operation: take a number n and find its prime factors. Reverse the digits of every prime factor (for example, replace 17 by 71). Multiply the factors respecting multiplicities. For example, if the original number was 17^2*43^3, the new product will be 71^2*34^3. After that, reverse the resulting number.
LINKS
M. F. Hasler, Table of n, a(n) for n=1..5000. [From M. F. Hasler, Jun 24 2009]
T. Khovanova, Turning Numbers Inside Out [From Tanya Khovanova, Jul 07 2009]
FORMULA
a(p) = p, for prime p.
From M. F. Hasler, Jun 25 2009: (Start)
a( p*10^k ) = p for any prime p.
Proof: if gcd( p, 2*5) = 1, then a( p * 10^k ) = R( R(p) * R(2)^k * R(5)^k ) = R( R(p) * 10^k ) = R(R(p)) = p;
if gcd(p, 2*5) = 2, then p=2 and a( p * 10^k ) = R( R(2)^(k+1) * R(5)^k ) = R( 2 * 10^k ) = 2 = p and mutatis mutandis for gcd(p, 2*5) = 5. (End)
EXAMPLE
a(34) = 241, because 34 = 2*17, f(34) = 2*71 = 142, and reversing gives 241.
MAPLE
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: A161594 := proc(n) digrev(A071786(n)) ; end: seq(A161594(n), n=1..80) ; # R. J. Mathar, Jun 16 2009
# second Maple program:
r:= n-> (s-> parse(cat(seq(s[-i], i=1..length(s)))))(""||n):
a:= n-> r(mul(r(i[1])^i[2], i=ifactors(n)[2])):
seq(a(n), n=1..100); # Alois P. Heinz, Jun 19 2017
MATHEMATICA
reversepower[{n_, k_}] := FromDigits[Reverse[IntegerDigits[n]]]^k f[n_] := FromDigits[ Reverse[IntegerDigits[Times @@ Map[reversepower, FactorInteger[n]]]]] Table[f[n], {n, 100}]
Table[IntegerReverse[Times@@Flatten[Table[IntegerReverse[#[[1]]], #[[2]]]& /@FactorInteger[n]]], {n, 100}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 21 2016 *)
PROG
(PARI) R=A004086; A161594(n)={n=factor(n); n[, 1]=apply(R, n[, 1]); R(factorback(n))} \\ M. F. Hasler, Jun 24 2009. Removed code for R here, see A004086 for most recent & efficient version. - M. F. Hasler, May 11 2015
(Haskell) a161594 = a004086 . a071786 -- Reinhard Zumkeller, Oct 14 2011
(Python)
from math import prod
from sympy import factorint
def f(n): return prod(int(str(p)[::-1])**e for p, e in factorint(n).items())
def R(n): return int(str(n)[::-1])
def a(n): return 1 if n == 1 else R(f(n))
print([a(n) for n in range(1, 73)]) # Michael S. Branicky, Mar 28 2022
CROSSREFS
KEYWORD
AUTHOR
J. H. Conway & Tanya Khovanova, Jun 14 2009
EXTENSIONS
Simpler definition from R. J. Mathar, Jun 16 2009
Edited by N. J. A. Sloane, Jun 23 2009
STATUS
approved